EN 13001-3-3

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3-3.

3-3.

(prCEN/TS 13001-3-3:2007, IDT)

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621.873.21.3(083.74) 53.020.20 03 IDT

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3-3.

3-3.

Cranes

General design

Part 3-3. Limit states and proof of competence of wheel/rail contacts

2010-01-01

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1 Scope

This Part 3-3 of EN 13001 is to be used together with Part 1 and Part 2 and as such they specify generalconditions, requirements and methods to prevent mechanical hazards of wheel/rail contacts of cranes by

design and theoretical verification. This standard covers steel and cast iron wheels.

The following is a list of significant hazardous situations and hazardous events that could result in risks topersons during normal use and foreseeable misuse. Clauses 5 to 6 of this standard are necessary to reduceor eliminate the risks associated with the following hazard:

Exceeding the limits of strength.

This Technical Specification is applicable to cranes that are manufactured after the date of approval by CENof this standard, and serves as reference base for the Technical Specifications for particular crane types.

NOTE CEN/TS 13001-3-3 deals only with limit state method according to EN 13001-1.

2 Normative references

The following referenced documents are indispensable for the application of this document. For datedreferences, only the edition cited applies. For undated references, the latest edition of the referenceddocument (including any amendments) applies.

EN 13001-1, Cranes — General Design — Part 1: General principles and requirements

EN 13001-2, Cranes — General Design — Part 2: Load actions

EN ISO 6506-1, Metallic materials — Brinell hardness test — Part 1: Test method (ISO 6506-1:2005)

EN ISO 12100-1:2003, Safety of machinery — Basic concepts, general principles for design — Part 1: Basicterminology, methodology (ISO 12100-1:2003)

ISO 4306-1:1990, Cranes — vocabulary — Part 1: General

ISO 12488-1, Cranes — Tolerances for wheels and travel and traversing tracks — Part 1: General

3 Terms, definitions, symbols and abbreviations

3.1 Terms and definitions

For the purposes of this Technical Specification, the terms and definitions given in EN ISO 12100-1:2003,EN 1991-1:1994 and Clause 6 of ISO 4306-1:1990, and the following apply.

Unit-conform hardness Some formulas used for calculations within this document refer to a so called “unit-conform hardness” HB

*

based on the Brinell hardness HBW given as a value without unit according to EN ISO 6506-1. The unit ofHB* has to match with the unit of the modulus of elasticity used in the calculation. Using SI-units, the unit-conform hardness is given by

2

*

mm

N HBW HB ⋅= (1)

where

HB* is the unit-conform Hardness;

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HBW is the value of the Brinell hardness.

EXAMPLE A Brinell hardness HB of 300 results into a unit-conform hardness HB* = 300 N/mm².

NOTE Annex B provides a table of hardness conversion.

3.2 Symbols and abbreviations

For the purposes of this Technical Specification, the symbols and abbreviations given in Table 1 apply.

Table 1 — Symbols and abbreviations

Symbols, abbreviations Description

b Load-bearing width

w D Wheel diameter

m E Mean modulus of elasticity

r E Modulus of elasticity of the rail

w E Modulus of elasticity of the wheel

F Wheel load

f Rd, F Limit design contact force for fatigue

sRd, F Limit design contact force

f Sd, F Design contact force for fatigue

if,Sd, F Design contact force in contact i

sSd, F Design contact force

u F Minimum contact force

f f Factors of further influence in fatigue

f1 f Decreasing factor for edge pressure in fatigue

f2 f Decreasing factor for non-uniform pressure distribution in fatigue

f3 f Decreasing factor for skewing in fatigue

f4 f Matching material factor in fatigue

f5 f Decreasing factor for driven wheels in fatigue

y f Yield point

1 f Decreasing factor for edge pressure

2 f Decreasing factor for non-uniform pressure distribution

4r 4w, f f Matching materials factor for wheel or rail in fatigue

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Table 1 (continued)

Symbols, abbreviations Description

HBW Brinell Hardness

* HB Unit-conform hardness

* HR Rockwell hardness

* HV Vickers hardness

i Index of one rolling contact with if,Sd, F

Di Number of rolling contacts at reference point

toti Total number of rolling contacts during the useful life of wheel or rail

m Exponent for wheel/rail contacts

ck Contact force spectrum factor

kr Radius of the rail surface or the second wheel radius

3r Radius of the edge

c s Contact force history parameter

cS Classes of contact force history parameter c s

w Width of projecting non-contact area

ml,mp Z Z Depth of point of maximum shear for point or line contact

Skewing angle

gα Part of the skewing angle α due to the slack of the guide

tα Part of the skewing angle α due to tolerances

wα Part of the skewing angle α due to wear

cf γ Minimum contact resistance factor

mγ General resistance coefficient; 1.1m =γ

nγ Risk coefficient

pγ Partial safety factors

v Radial strain coefficient ( 3,0=v for steel)

cv Relative total number of rolling contacts

φ Dynamic factors (see EN 13001-2)

4 General

In all cranes, wheels and rails (or wheels and supporting area or guide rollers and guide means) are stressedby loads (described by a load spectrum) and by rolling contacts. Both constitute the contact force historyparameter

c s (see 6.3.3). The contact force history parameter is used for the selection of wheels and rails. It is

independent of time.

NOTE 1 For the purpose of this standard guide rollers and their guiding means as well as wheels running on thesurface of a member shall be considered as wheels and rails.

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The proof of competence for static strength and the proof of competence for fatigue strength shall be fulfilledfor the selection of wheels and rails. This standard is for design purposes only and should not be seen as aguarantee of actual performance.

NOTE 2 This standard is applicable for metallic wheel/rail contacts only. Other materials require the applicability of the

Hertz theory of contact pressure.

5 Proof of static strength

5.1 General

For the proof of static strength of all wheel/rail contacts it shall be proven that for all relevant loadcombinations of EN 13001-2:

sRd,sSd, F F ≤ (2)

where

sSd, F is the design contact force;

sRd, F s the limit design contact force.

5.2 Design contact force

The design contact force sSd, F of all wheel/rail contacts shall be calculated for all relevant load combinations

of EN 13001-2, taking into account the respective dynamic factors φ , partial safety factors pγ and where

required the risk coefficient nγ . The most unfavourable load effects from the position of the mass of the hoistload and from the crane configuration shall be taken into account.

5.3 Static limit design contact force

5.3.1 General

A contact force of the magnitude of the static limit design contact force sRd, F causes permanent radial

deformation of 0,02 % of the wheel radius.

The static limit design contact force sRd, F depends on:

materials properties (modulus of elasticity and hardness) of wheel and rail;

contact case (point contact or line contact);

geometry (radii of wheel and rail);

decreasing effects (stiffness, edge effects).

5.3.2 Equivalent modulus of elasticity

When the elastic modules of wheel and rail are different, the equivalent modulus of elasticity shall be

calculated as

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r w

r wm

2

E E

E E E

+

⋅⋅= (3)

where

m E is the equivalent modulus of elasticity ;

w E is the modulus of elasticity of the wheel;

r E is the modulus of elasticity of the rail.

(In case w E = r E then of course m E = w E = r E )

Values of the elastic modules for selected materials are given in Table 2.

Table 2 — Values of elastic modules for selected materials

Material of wheel, material of rail modulus of elasticity of the wheel in N/mm2

Steel 210 000

cast iron 176 000

5.3.3 Hardness

The static limit design contact force shall be calculated in terms of the unit-conform material hardness HB*

(see 0) in the contact areas.

If the hardness of wheel and rail are different, the lower value shall be taken.

For hardened materials it shall be ensured that the hardness assumed in calculations reaches deeper into thematerial than the point of maximum shear.

5.3.4 Point contact

Formula (4) gives the static limit design contact force sRd, F for cases of point contact the point of maximum

shear is situated at depth mp Z below the surface.

Typical point contacts are shown in Figure 1.

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Key

( ) ( )( )

2

12m

233*

m

sRd,

kw

13

5,110

1

+⋅

−⋅⋅

⋅=r D

E

v HB F

π

γ (4)

( )( )

kw

12m

2

m

*

mp

127,4

r D E

HB z

+⋅

−⋅⋅⋅⋅= ν π

γ (5)

where

sRd, F is the static limit design contact force for point contact;

mp z is the depth of point of maximum shear;

m E is the equivalent elasticity modulus;

v is the radial strain coefficient ( v = 0,3 for steel);

w D is the wheel diameter;

kr is the radius of the rail surface or the second wheel radius (see Figure 1);

∗ HB is the unit-conform hardness (see chapter 0) at the point of maximum shear;

mγ is the general resistance coefficient; mγ =1,1.

Figure 1 — Point contact

5.3.5 Line contact

5.3.5.1 General

Formula 6 gives the static limit design contact force sRd, F for cases of line contact. The point of maximum

shear is situated at depthml Z below the surface.

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Typical line contacts are shown in Figure 2.

Key

( ) ( ) 21m

2

w2*

m

sRd, 151 f f E

vb D HB F ⋅⋅−⋅⋅⋅⋅= π γ

(6)

( )m

2w

m

*

mlE

v1DHB8,7z

−⋅⋅

γ ⋅= (7)

where

sRd, F is the static limit design contact force for line contact;

ml z is the depth of point of maximum shear;

m E is the mean modulus of elasticity;

v is the radial strain coefficient ( v = 0,3 for steel );


b is the load-bearing width (see Figure 2);

∗ HB is the unit-conform hardness (see chapter 0) at the point of maximum shear;

mγ is the general resistance coefficient; mγ =1,1;

1 f is the decreasing factor for edge pressure;

2 f

is the decreasing factor for non-uniform pressure distribution.

Figure 2 — Line contact

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5.3.5.2 Edge pressure

Sharp edges at the end of the contact line of wheel or rail decrease the limit design contact force. This effect

is taken into account by factor1

f , given in Table 3.

Figure 3 — Edge pressure

Table 3 — Factor 1 f for edge pressure

edgewr /3 1 f

1,0/3 ≤wr 75,0

8,0/1,0 3

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6 Proof of fatigue strength

6.1 General

For the proof of fatigue strength of all wheel/rail contacts it shall be proven that for each wheel and for allpoints on the rails

Rd,f Sd,f F F ≤ (8)

where

Sd,f F is the design contact force for fatigue;

Rd,f F is the limit design contact force for fatigue.

6.2 Design contact force

The design contact force Sd,f F shall be calculated for regular loads (load combinations A of EN 13001-2), with

the respective dynamic factors φ , partial safety factors pγ , and risk coefficient nγ set to 1. The skewing

forces acting on guide rollers shall be considered as regular loads.

6.3 Limit design contact force

6.3.1 Basic formula

The limit design contact force Rd,f F shall be calculated for wheels and rails separately by

f

cf c

uRd,f f

s

F F

m⋅

⋅=

γ (9)

where

u F is the minimum contact force;

c s is the contact force history parameter;

cf γ is the minimum contact resistance factor;

cf γ = 1,1;

f f is the factor of further influences;

m is the exponent for wheel/rail contacts;

m = 3 for cases of point contact and

m = 10 / 3 for cases of line contact.

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6.3.2 Minimum contact force

The limit design contact force of a wheel or rail stressed by rolling contact fatigue is characterized by the

minimum contact force u F which represents the fatigue strength under 6,4 x 106 rolling contacts under

constant contact force and a probability of survival (i.e. avoiding cracks, pitting, excessive wear) of 90 % . Fora wheel one revolution is equivalent to one rolling contact, whereas for a selected point in the rail the passingover of any wheel represents one rolling contact. In cases where the wheel is not rolling but the load isfluctuating, one load cycle shall be considered as one rolling contact.

The minimum contact force for wheel/rail is dependent upon either the surface hardness or on the yield point

as given in Table 5. The lower value of u F obtained from the equations in Table 5 shall be taken into account.

u F is calculated separately for wheel and rail.

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Table 5 — Minimum contact force u F

u

F related to the surface hardness of

wheel or railu

F related to the yield point of the wheel

or rail material

Point contact ( ) ( )( )

2

12m

233*

kw

13

5,12,5

+⋅

−⋅⋅

⋅⋅

r D E

v HB

π ( ) ( )

( )

2

12m

23

3

y

kw

13

5,16,1

+⋅

−⋅⋅

⋅⋅

r D E

v f

π

Line contact ( ) ( )m

2

w2* 10,3 E

vb D HB

−⋅⋅⋅⋅⋅π

( ) ( )m

2

w2 18,1 E

vb D f y

−⋅⋅⋅⋅⋅π

where

m E is the equivalent elasticity modulus;

v is the radial strain coefficient ( v = 0,3);


kr is the radius of the rail surface or the second wheel radius (see Figure 1);

∗ HB is the unit-conform hardness (see clause 0);

y f is the yield point of the material at the depth of maximum shear (if surface hardened, before that process);

b is the load-bearing width (see Figure 2).

6.3.3 Contact force history parameter

In analogy to stress history parameter (see EN 13001-1), the contact force history parameter is given by

ccc vk s ⋅= (10)

where

ck is the contact force spectrum factor;

cv is the relative total number of rolling contacts.

The contact force history parameter shall be determined either by direct use of formula (10) or simplified

(based on experience) by selection of a class cS from Table 6. If Table 6 is used, then in formula (9) the

exponent m shall be set to 3, independent of the contact case.

Table 6 — Classes cS of contact force history parameter c s

Class 0cS 1cS 2cS 3cS 4cS 5cS 6cS 7cS 8cS 9cS

c s 0,008 0,016 0,032 0,063 0,125 0,25 0,5 1,0 2,0 4,0

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6.3.4 Contact force spectrum factor

The contact force spectrum factorc

k is calculated by

=

⋅=

toti

1i Sd,f

Sd,f,

totc /1

m

i

F

F ik (11)

where

i is the index of one rolling contact with i f Sd F ,, ;

toti is the total number of rolling contacts during the specified life of wheel or rail (in general based

upon the life of component or crane);

iSd,f, F is the design contact force in contact i ;

Sd,f F is the maximum design contact force;

m is the exponent for wheel/rail contacts.

6.3.5 Relative total number of rolling contacts

The relative total number of rolling contacts cv is calculated by

D

totc

i

iv = (12)

where

toti is the total number of rolling contacts during the useful life of wheel or rail;

Di is the number of rolling contacts at reference point:6

D 104,6 ⋅=i .

6.4 Factor of further influences

6.4.1 Basic formula

The factor f f takes into account further influences on the limit design contact force:

5f f43f 2f f1f f f f f f f ⋅⋅⋅⋅= (13)

where

1f f to f5 f are the factors of influences as given in 6.4.2 to 6.4.6.

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6.4.2 Edge pressure

Due to lateral movements of wheels the edge pressure acting on the surface opposite the edge may be

neglected and the factor f1 f is set to 1. For the surface with the edge radius 3r (see Figure 2),

1f1 f f = (14)

where

1 f is the factor for edge pressure as given in 5.3.5.2.

6.4.3 Pressure distribution

For the proof of fatigue strength the pressure distribution may be neglected and f2 f set to 1.

6.4.4 Skewing

A skewing wheel causes wear of wheel and rail and thus shortens the useful life. The wear is increased over-

proportionally in relation to the skewing angle α . This effect is taken into account by factor f3 f .

13f = f for ≤ 50/00

3f3

5

α = f for >α 5 0/00 (15)

where

twg α α α α ++= is the skewing angle of the crane in0/00, calculated according to EN 13001-2.

The part of the skewing angle due to tolerances tα shall be chosen according to the tolerance as given in

Table 7.

Table 7 — Alignment angle of single wheel or roller

Alignment Tolerance class 1 Tolerance class 2 Tolerance class 3 Tolerance class 4

α t 1,5 0/00 2,5 0/00 3,5 0/00 4,5 0/00

6.4.5 Matching materials

Wear and mechanical abrasion of wheel and rail depend considerably on the combination of mechanicalproperties (e.g. type of material, hardening, ultimate strength) of wheel and rail.

Matching materials cause equal wear of a wheel and a rail per rolling contact. Non-matching materials willincrease wear of one partner and decrease wear of the other partner. This may be taken into account by

factor f4 f .

For a particular chosen pair of wheel and rail materials, 4f f shall be chosen such that:

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r 4

w4

1

f f =

where

4wf4 f f = is the matching materials factor for a wheel,

r 44f f f = is the matching materials factor for a rail.

The factor 4f f shall be chosen from experience in the range between 0,66 and 1,5. Examples are given in

informative Annex C.

6.4.6 Mechanical drive factor

In an unclean environment the mechanical abrasion effects on the driven wheels may be taken into account

by factor f5 f .

95,0f5 = f for driven wheels in unclean environment, (17)

0,1f5 = f for non-driven wheels or wheels in clean environment.

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Annex A(informative)

Selection of suitable set of crane standards for a given application

Table A.1

Is there a product standard in the following list that suits the application?

EN 13000:2004 Cranes — Mobile cranes

EN 14439:2006 Cranes — Tower cranes

EN 14985:2007 Cranes — Slewing jib cranes

prEN 15011:2006 Cranes — Bridge and gantry cranes

EN 15056:2006 Cranes — Requirements for container handling spreaders

EN 13852-1:2004 Cranes — Offshore cranes — Part 1: General purpose offshore cranes

EN 13852-2:2004 Cranes — Offshore cranes — Part 2: Floating cranes

EN 14492-1:2006 Cranes — Power driven winches and hoists — Part 1: Power driven winches

EN 14492-2:2006 Cranes — Power driven winches and hoists — Part 2: Power driven hoists

EN 12999: 2002 Cranes — Loader cranes

EN 13157: 2004 Cranes — Safety — Hand powered Lifting equipment

EN 13155: 2003 Cranes — Safety — Non-fixed load lifting attachments

EN 14238:2004 Cranes — Manually controlled load manipulating devices

YES NOUse it directly, plus the standards

that are referred to

Use the following:

EN 13001-1:2004 Cranes — General design — Part 1: General principles and requirements

EN 13001-2:2004 Cranes — General design — Part 2: Load actions

CEN/TS 13001-3-1: 2004 Cranes — General design — Part 3-1: Limit states and proof of competence of steel structures

CEN/TS 13001-3-2: 2004 Cranes — General design — Part 3-2: Limit states and proof of competence of wire ropes inreeving systems

prCEN/TS 13001-3-3:2007 Cranes — General design — Part 3-3: Limit states and proof of competence of wheel/ railcontacts

EN 13135-1:2003 Cranes — Safety – Design — Requirements for Equipment — Part 1: Electrotechnicalequipment

EN 13135-2:2004 Cranes — Requirements for Equipment — Part 2: Non-electrotechnical equipment

EN 13557:2003 Cranes — Controls and control stations

EN 12077-2:1998 Cranes safety — Requirements for health and safety — Part 2: Limiting and indicating devices

EN 13586: 2004 Cranes — Access

EN 14502-1:2005 Cranes — Equipment for the lifting of persons — Part 1: Suspended baskets

EN 14502-2:2005 Cranes — Equipment for the lifting of persons — Part 2: Elevating control stations

EN 12644-1:2001 Cranes — Information for use and testing — Part 1: Instructions

EN 12644-2:2000 Cranes — Information for use and testing — Part 2: Marking

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Annex B(informative)

Conversion table of hardness

Table B.1 — Conversion table of hardness

Hardness Hardness

HV HBW HRA HRB HRC HRD HV HBW HRA HRC HRD

80 76 350 332,5 68,1 35,5 51,9

85 80,7 360 342 68,7 36,6 52,8

90 85,5 370 351,5 69,2 37,7 53,8

95 90,2 380 361 69,8 38,8 54,4

100 95 390 370,5 70,3 39,8 55,2

105 99,8 400 380 70,8 40,8 56

110 104,5 62 410 389,5 71,4 41,8 56,8

115 109,3 64,6 420 399 71,8 42,7 57,5

120 114 67 430 408,5 72 43,6 58,2

125 118,8 69 440 418 72,3 44,5 58,8

130 123,5 71 450 423 73,3 45,3 59,4

135 128,3 73,1 460 432 73,6 46,1 60,1

140 133 75,1 470 442 74,1 46,9 60,7

145 137,8 77 480 450 74,5 47,7 61,3

150 142,5 78,8 490 456 74,9 48,4 61,6

155 147,3 80,5 500 466 75,3 49,1 62,2

160 152 82,1 510 475 75,7 49,8 62,9

165 156,8 83,5 520 483 76,1 50,5 63,5

170 161,5 85 530 492 76,4 51,1 63,9

175 166,3 86,1 540 500 76,7 51,7 64,4

180 171 87,3 550 509 77 52,3 64,8

185 175,8 88,5 560 517 77,4 53 65,4

190 180,5 89,6 570 526 77,8 53,6 65,8

where

HV is the Vickers hardness;

HBW is the Brinell hardness;

HR is the Rockwell hardness as follows HRA, HRB, HRC, HRD.

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Annex C (informative)

Examples for matching materials factor

Table C.1 – Examples for matching materials factor

Material number wheel a (name)

Material number rail a

(name) w4 f r 4 f

1.0558 (GS-60) 1.0527 (C56) 1 1

1.0558 (GS-60) 1.0624 (R0900Mn) 0,8 1,25

1.7225 hardened and tempered(42CrMo4)

1.0527 (C56) 1 1


1.0624 (R0900Mn) 0,87 1,15


1.0527 (C56) 1,25 0,8


1.0624 (R0900Mn) 1 1

1.6956 hardened (33NiCrMo14-5) 1.0527 (C56) 1,3 0,77

1.6956 hardened (33NiCrMo14-5) 1.0624 (R0900Mn) 1,05 0,95

1.7225 hardened (42CrMo4) 1.0527 (C56) 1,5 0,66

1.7225 hardened (42CrMo4) 1.0624 (R0900Mn) 1,15 0,87

1.7229 hardened (61CrMo4) 1.0527 (C56) 1,50 0,66

1.7229 hardened (61CrMo4) 1.0624 (R0900Mn) 1,15 0,87

a Numbers according to the “Register of European Steels”.

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Bibliography

[1] Niemann, G.: Maschinenelemente Band I, 2. Auflage, Springer Verlag Berlin.

[2] Hesse, W.: Verschleißverhalten des Laufrad-Schiene-Systems fördertechnischer Anlagen, Diss. Ruhr-Universität Bochum 1983.

[3] Scheffler, M.: Grundlagen der Fördertechnik — Elemente und Triebwerke. Vieweg Verlag 1994.

[4] Calcul en fatigue du contact galet/rail, 1B2302 et 1B2303, J-F. FLAVENOT, CETIM, Juin 2003

[5] A. EKBERG, E. KABO and H. ANDERSON — An engineering model for prediction of rolling, contactfatigue of railway wheels, Fatigue Fracture Engineering Materials and Structures 25 (2002), pages899-909

[6] EN 1990:2002, Eurocode, Basis of structural design

Documents

EN 13001-3-3