EN 13001-3-3

ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɋɌȺɇȾȺɊɌ ɊȿɋɉɍȻɅɂɄɂ ȻȿɅȺɊɍɋɖ

ɋɌȻ prCEN/TS 13001-3-3-2009

ɄɊȺɇɕ ɈȻɓȺə ɄɈɇɋɌɊɍɄɐɂə ɑɚɫɬɶ 3-3. ɉɪɟɞɟɥɶɧɵɟ ɫɨɫɬɨɹɧɢɹ ɢ ɩɨɞɬɜɟɪɠɞɟɧɢɟ ɛɟɡɨɩɚɫɧɨɫɬɢ ɤɨɥɟɫɧɵɯ ɢ ɪɟɥɶɫɨɜɵɯ ɤɨɧɬɚɤɬɨɜ

ɄɊȺɇɕ ȺȽɍɅɖɇȺə ɄȺɇɋɌɊɍɄɐɕə ɑɚɫɬɤɚ 3-3. Ƚɪɚɧɿɱɧɵɹ ɫɬɚɧɵ ɿ ɩɚɰɜɹɪɞɠɷɧɧɟ ɛɹɫɩɟɤɿ ɤɨɥɚɜɵɯ ɿ ɪɷɣɤɚɜɵɯ ɤɚɧɬɚɤɬɚʆ

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

ɂɡɞɚɧɢɟ ɨɮɢɰɢɚɥɶɧɨɟ

Ƚɨɫɫɬɚɧɞɚɪɬ Ɇɢɧɫɤ

ɋɌȻ prCEN/TS 13001-3-3-2009 ɍȾɄ 621.873.21.3(083.74)

ɆɄɋ 53.020.20

Ʉɉ 03

IDT

Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɤɪɚɧɵ, ɨɛɳɢɟ ɤɨɧɫɬɪɭɤɰɢɢ, ɩɪɟɞɟɥɶɧɵɟ ɫɨɫɬɨɹɧɢɹ, ɛɟɡɨɩɚɫɧɨɫɬɶ, ɤɨɥɟɫɧɵɟ ɤɨɧɬɚɤɬɵ, ɪɟɥɶɫɨɜɵɟ ɤɨɧɬɚɤɬɵ

ɉɪɟɞɢɫɥɨɜɢɟ ɐɟɥɢ, ɨɫɧɨɜɧɵɟ ɩɪɢɧɰɢɩɵ, ɩɨɥɨɠɟɧɢɹ ɩɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɦɭ ɪɟɝɭɥɢɪɨɜɚɧɢɸ ɢ ɭɩɪɚɜɥɟɧɢɸ ɜ ɨɛɥɚɫɬɢ ɬɟɯɧɢɱɟɫɤɨɝɨ ɧɨɪɦɢɪɨɜɚɧɢɹ ɢ ɫɬɚɧɞɚɪɬɢɡɚɰɢɢ ɭɫɬɚɧɨɜɥɟɧɵ Ɂɚɤɨɧɨɦ Ɋɟɫɩɭɛɥɢɤɢ Ȼɟɥɚɪɭɫɶ «Ɉ ɬɟɯɧɢɱɟɫɤɨɦ ɧɨɪɦɢɪɨɜɚɧɢɢ ɢ ɫɬɚɧɞɚɪɬɢɡɚɰɢɢ» 1 ɉɈȾȽɈɌɈȼɅȿɇ ɉɈ ɍɋɄɈɊȿɇɇɈɃ ɉɊɈɐȿȾɍɊȿ ɧɚɭɱɧɨ-ɩɪɨɟɤɬɧɨɩɪɨɢɡɜɨɞɫɬɜɟɧɧɵɦ ɪɟɫɩɭɛɥɢɤɚɧɫɤɢɦ ɭɧɢɬɚɪɧɵɦ ɩɪɟɞɩɪɢɹɬɢɟɦ «ɋɬɪɨɣɬɟɯɧɨɪɦ» (Ɋɍɉ «ɋɬɪɨɣɬɟɯɧɨɪɦ») ȼɇȿɋȿɇ Ɇɢɧɢɫɬɟɪɫɬɜɨɦ ɚɪɯɢɬɟɤɬɭɪɵ ɢ ɫɬɪɨɢɬɟɥɶɫɬɜɚ Ɋɟɫɩɭɛɥɢɤɢ Ȼɟɥɚɪɭɫɶ 2 ɍɌȼȿɊɀȾȿɇ ɂ ȼȼȿȾȿɇ ȼ ȾȿɃɋɌȼɂȿ ɩɨɫɬɚɧɨɜɥɟɧɢɟɦ Ƚɨɫɫɬɚɧɞɚɪɬɚ Ɋɟɫɩɭɛɥɢɤɢ Ȼɟɥɚɪɭɫɶ ɨɬ ________________ ʋ _______ ȼ ɧɚɰɢɨɧɚɥɶɧɨɦ ɤɨɦɩɥɟɤɫɟ ɬɟɯɧɢɱɟɫɤɢɯ ɧɨɪɦɚɬɢɜɧɵɯ ɩɪɚɜɨɜɵɯ ɚɤɬɨɜ ɜ ɨɛɥɚɫɬɢ ɚɪɯɢɬɟɤɬɭɪɵ ɢ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɧɚɫɬɨɹɳɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɫɬɚɧɞɚɪɬ ɜɯɨɞɢɬ ɜ ɛɥɨɤ 1.03 «Ɉɪɝɚɧɢɡɚɰɢɹ ɫɬɪɨɢɬɟɥɶɧɨɝɨ ɩɪɨɢɡɜɨɞɫɬɜɚ» 3 ɇɚɫɬɨɹɳɢɣ ɫɬɚɧɞɚɪɬ ɢɞɟɧɬɢɱɟɧ ɦɟɠɞɭɧɚɪɨɞɧɨɦɭ ɫɬɚɧɞɚɪɬɭ prCEN/TS 13001-3-3:2007 Cranes - General design - Part 3-3: Limit states and proof of competence of wheel/rail contacts (Ʉɪɚɧɵ. Ɉɛɳɚɹ ɤɨɧɫɬɪɭɤɰɢɹ. ɑɚɫɬɶ 3-3. ɉɪɟɞɟɥɶɧɵɟ ɫɨɫɬɨɹɧɢɹ ɢ ɩɨɞɬɜɟɪɠɞɟɧɢɟ ɛɟɡɨɩɚɫɧɨɫɬɢ ɤɨɥɟɫɧɵɯ ɢ ɪɟɥɶɫɨɜɵɯ ɤɨɧɬɚɤɬɨɜ). Ɇɟɠɞɭɧɚɪɨɞɧɵɣ ɫɬɚɧɞɚɪɬ ɪɚɡɪɚɛɨɬɚɧ ɬɟɯɧɢɱɟɫɤɢɦ ɤɨɦɢɬɟɬɨɦ ɩɨ ɫɬɚɧɞɚɪɬɢɡɚɰɢɢ CEN/TS 96 «Ʉɪɚɧɵ – ɛɟɡɨɩɚɫɧɨɫɬɶ» ɉɟɪɟɜɨɞ ɫ ɚɧɝɥɢɣɫɤɨɝɨ ɹɡɵɤɚ (ɟn). Ɉɮɢɰɢɚɥɶɧɵɟ ɷɤɡɟɦɩɥɹɪɵ ɦɟɠɞɭɧɚɪɨɞɧɨɝɨ ɫɬɚɧɞɚɪɬɚ, ɧɚ ɨɫɧɨɜɟ ɤɨɬɨɪɨɝɨ ɩɨɞɝɨɬɨɜɥɟɧ ɧɚɫɬɨɹɳɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɫɬɚɧɞɚɪɬ, ɢ ɦɟɠɞɭɧɚɪɨɞɧɵɯ ɫɬɚɧɞɚɪɬɨɜ, ɧɚ ɤɨɬɨɪɵɟ ɞɚɧɵ ɫɫɵɥɤɢ, ɢɦɟɸɬɫɹ ɜ ɇɚɰɢɨɧɚɥɶɧɨɦ ɮɨɧɞɟ ɌɇɉȺ. ɋɬɟɩɟɧɶ ɫɨɨɬɜɟɬɫɬɜɢɹ – ɢɞɟɧɬɢɱɧɚɹ (IDT) 4 ȼȼȿȾȿɇ ȼɉȿɊȼɕȿ

ɇɚɫɬɨɹɳɢɣ ɫɬɚɧɞɚɪɬ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɜɨɫɩɪɨɢɡɜɟɞɟɧ, ɬɢɪɚɠɢɪɨɜɚɧ ɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧ ɜ ɤɚɱɟɫɬɜɟ ɨɮɢɰɢɚɥɶɧɨɝɨ ɢɡɞɚɧɢɹ ɛɟɡ ɪɚɡɪɟɲɟɧɢɹ Ƚɨɫɫɬɚɧɞɚɪɬɚ Ɋɟɫɩɭɛɥɢɤɢ Ȼɟɥɚɪɭɫɶ ɂɡɞɚɧ ɧɚ ɪɭɫɫɤɨɦ ɹɡɵɤɟ II

ɋɌȻ prCEN/TS 13001-3-3-2009

ȼɜɟɞɟɧɢɟ

ɇɚɫɬɨɹɳɢɣ

ɫɬɚɧɞɚɪɬ

ɫɨɞɟɪɠɢɬ

ɬɟɤɫɬ

ɦɟɠɞɭɧɚɪɨɞɧɨɝɨ

ɫɬɚɧɞɚɪɬɚ

prCEN/TS 13001-3-3:2007 ɧɚ ɹɡɵɤɟ ɨɪɢɝɢɧɚɥɚ ɢ ɟɝɨ ɩɟɪɟɜɨɞ ɧɚ ɪɭɫɫɤɢɣ ɹɡɵɤ (ɫɩɪɚɜɨɱɧɨɟ ɩɪɢɥɨɠɟɧɢɟ Ⱦ.Ⱥ). ȼɜɟɞɟɧ ɜ ɞɟɣɫɬɜɢɟ, ɤɚɤ ɫɬɚɧɞɚɪɬ, ɧɚ ɤɨɬɨɪɵɣ ɟɫɬɶ ɫɫɵɥɤɚ

ɜ ȿɜɪɨɤɨɞɟ

EN 1993-6:2005.

ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɋɌȺɇȾȺɊɌ ɊȿɋɉɍȻɅɂɄɂ ȻȿɅȺɊɍɋɖ ɄɊȺɇɕ ɈȻɓȺə ɄɈɇɋɌɊɍɄɐɂə ɑɚɫɬɶ 3-3. ɉɪɟɞɟɥɶɧɵɟ ɫɨɫɬɨɹɧɢɹ ɢ ɩɨɞɬɜɟɪɠɞɟɧɢɟ ɛɟɡɨɩɚɫɧɨɫɬɢ ɤɨɥɟɫɧɵɯ ɢ ɪɟɥɶɫɨɜɵɯ ɤɨɧɬɚɤɬɨɜ ɄɊȺɇɕ ȺȽɍɅɖɇȺə ɄȺɇɋɌɊɍɄɐɕə ɑɚɫɬɤɚ 3-3. Ƚɪɚɧɿɱɧɵɹ ɫɬɚɧɵ ɿ ɩɚɰɜɹɪɞɠɷɧɧɟ ɛɹɫɩɟɤɿ ɤɨɥɚɜɵɯ ɿ ɪɷɣɤɚɜɵɯ ɤɚɧɬɚɤɬɚʆ

Cranes General design Part 3-3. Limit states and proof of competence of wheel/rail contacts Ⱦɚɬɚ ɜɜɟɞɟɧɢɹ 2010-01-01

III

prCEN/TS 13001-3-3:2007 (E)

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 general conditions, 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 to persons during normal use and foreseeable misuse. Clauses 5 to 6 of this standard are necessary to reduce or 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 CEN of this standard, and serves as reference base for the Technical Specifications for particular crane types. NOTE

2

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

Normative references

The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN 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: Basic terminology, 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 3.1

Terms, definitions, symbols and abbreviations 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 of HB* has to match with the unit of the modulus of elasticity used in the calculation. Using SI-units, the unitconform hardness is given by

HB * = HBW ⋅

N mm 2

(1)

where *

HB

is the unit-conform Hardness;

1

prCEN/TS 13001-3-3:2007 (E)

HBW EXAMPLE NOTE

3.2

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

Annex B provides a table of hardness conversion.

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

b

Load-bearing width

Dw

Wheel diameter

Em

Mean modulus of elasticity

Er

Modulus of elasticity of the rail

Ew

Modulus of elasticity of the wheel

F

Wheel load

FRd,f

Limit design contact force for fatigue

FRd,s

Limit design contact force

FSd,f

Design contact force for fatigue

FSd,f,i

Design contact force in contact

FSd,s

Design contact force

i

Fu

Minimum contact force

ff

Factors of further influence in fatigue

f f1

Decreasing factor for edge pressure in fatigue

f f2

Decreasing factor for non-uniform pressure distribution in fatigue

f f3

Decreasing factor for skewing in fatigue

f f4

Matching material factor in fatigue

f f5

Decreasing factor for driven wheels in fatigue

fy

Yield point

f1

Decreasing factor for edge pressure

f2

Decreasing factor for non-uniform pressure distribution

f 4w, f 4r

2

Description

Matching materials factor for wheel or rail in fatigue

prCEN/TS 13001-3-3:2007 (E)

Table 1 (continued) Symbols, abbreviations

HBW

Brinell Hardness

HB *

Unit-conform hardness

HR *

Rockwell hardness

HV *

Vickers hardness

i

Index of one rolling contact with FSd, f,i

iD

Number of rolling contacts at reference point

itot

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

m

Exponent for wheel/rail contacts

kc

Contact force spectrum factor

rk

Radius of the rail surface or the second wheel radius

r3

Radius of the edge

sc

Contact force history parameter

Sc

Classes of contact force history parameter sc

w

Width of projecting non-contact area

Z mp , Z ml

4

Description

Depth of point of maximum shear for point or line contact

α

Skewing angle

αg

Part of the skewing angle

α

due to the slack of the guide

αt

Part of the skewing angle

α

due to tolerances

αw

Part of the skewing angle

α

due to wear

γ cf

Minimum contact resistance factor

γm

General resistance coefficient; γ m = 1.1

γn

Risk coefficient

γp

Partial safety factors

v

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

vc

Relative total number of rolling contacts

φ

Dynamic factors (see EN 13001-2)

General

In all cranes, wheels and rails (or wheels and supporting area or guide rollers and guide means) are stressed by loads (described by a load spectrum) and by rolling contacts. Both constitute the contact force history parameter sc (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 the surface of a member shall be considered as wheels and rails.

3

prCEN/TS 13001-3-3:2007 (E)

The proof of competence for static strength and the proof of competence for fatigue strength shall be fulfilled for the selection of wheels and rails. This standard is for design purposes only and should not be seen as a guarantee 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 load combinations of EN 13001-2:

FSd,s ≤ FRd,s

(2)

where

5.2

FSd,s

is the design contact force;

FRd,s

s the limit design contact force.

Design contact force

The design contact force

FSd,s 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

γp

and where

required the risk coefficient γ n . The most unfavourable load effects from the position of the mass of the hoist load 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

FRd,s causes permanent radial

deformation of 0,02 % of the wheel radius. The static limit design contact force

FRd,s 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

4

prCEN/TS 13001-3-3:2007 (E)

Em =

2 ⋅ E w ⋅ Er E w + Er

(3)

where

Em is the equivalent modulus of elasticity ; E w is the modulus of elasticity of the wheel;

(In case

Er

is the modulus of elasticity of the rail.

Ew

= Er then of course

Em = E w

= Er )

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

5.3.3

2

modulus of elasticity of the wheel in N/mm

Steel

210 000

cast iron

176 000

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 the material than the point of maximum shear. 5.3.4

Point contact

Formula (4) gives the static limit design contact force shear is situated at depth

FRd,s for cases of point contact the point of maximum

Z mp below the surface.

Typical point contacts are shown in Figure 1.

5

prCEN/TS 13001-3-3:2007 (E)

Key

FRd,s =

1

γm

zmp = 4,7 ⋅

(10 HB )

* 3

(

)

3 2 § π · ª 3 ⋅ 1− v º ⋅¨ ¸ ⋅ « » © 1,5 ¹ ¬« Em ⋅ D2w + r1k ¼»

(

(

HB * 2 ⋅ π ⋅ 1 − ν 2 ⋅ γ m Em ⋅ D2w + r1k

(

2

)

)

)

(4)

(5)

where

FRd,s

is the static limit design contact force for point contact;

z mp

is the depth of point of maximum shear;

Em

is the equivalent elasticity modulus;

v

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

Dw

is the wheel diameter;

rk

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;

γm

is the general resistance coefficient;

γ m =1,1.

Figure 1 — Point contact

5.3.5 5.3.5.1

Line contact General

Formula 6 gives the static limit design contact force shear is situated at depth Z ml below the surface.

6

FRd,s for cases of line contact. The point of maximum

prCEN/TS 13001-3-3:2007 (E)

Typical line contacts are shown in Figure 2.

Key

FRd,s =

1

γm

z ml = 7,8 ⋅

(5 HB )

* 2

(

⋅

π ⋅ Dw ⋅ b ⋅ (1 − v 2 )

HB* D w ⋅ 1 − v 2 ⋅ γm Em

Em

⋅ f1 ⋅ f 2

)

(6)

(7)

where

FRd,s

is the static limit design contact force for line contact;

z ml

is the depth of point of maximum shear;

Em

is the mean modulus of elasticity;

v

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

Dw

is the wheel diameter;

b

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

HB ∗

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

γm

is the general resistance coefficient;

γ m =1,1;

f1

is the decreasing factor for edge pressure;

f2

is the decreasing factor for non-uniform pressure distribution.

Figure 2 — Line contact

7

prCEN/TS 13001-3-3:2007 (E)

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 factor f1 , given in Table 3.

Figure 3 — Edge pressure Table 3 — Factor edge

f1 for edge pressure

r3 / w

f1

r3 / w ≤ 0,1

0,75

0,1< r3 / w < 0,8

[0,5 + 0,25 (r3 / w)]/ 0,7

r3 / w ≥ 0,8

1,0

where

w

is the width of the projecting non-contact area and

r3 is the radius of the edge.

5.3.5.3

Pressure distribution

An ideal uniform distribution requires sufficient elasticity of the rail fixation or support and/or wheels in hinged legs. Otherwise deformation of the crane structure (e.g. bending of main girders) or tolerances in rail alignment result in non-uniform pressure distribution, decreasing the limit design contact force. This effect is taken into account by factor f 2 , given in Table 4 (Tolerance classes according ISO 12488-1). Table 4 — Factor

wheels with self-aligning suspension rail mounted on elastic adjustment to the wheel

support

allowing

rail support not allowing adjustment to the wheel

8

f 2 for pressure distribution Tolerance class 1

Tolerance class 2

Tolerance class 3

Tolerance class 4

1,0

1,0

0,95

0,9

0,9

0,85

0,8

0,7

0,8

0,75

0,7

0,6

prCEN/TS 13001-3-3:2007 (E)

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 all points on the rails

FSd,f ≤ FRd,f

(8)

where

6.2

FSd,f

is the design contact force for fatigue;

FRd,f

is the limit design contact force for fatigue.

Design contact force

The design contact force

FSd,f shall be calculated for regular loads (load combinations A of EN 13001-2), with

the respective dynamic factors

φ , partial

safety factors

γp,

and risk coefficient

γn

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

FRd,f =

Fu m

s c ⋅ γ cf

FRd,f shall be calculated for wheels and rails separately by

⋅ ff

(9)

where

Fu is the minimum contact force; sc is the contact force history parameter;

γ cf

is the minimum contact resistance factor;

γ cf = 1,1; ff

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.

9

prCEN/TS 13001-3-3:2007 (E)

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 6 minimum contact force Fu which represents the fatigue strength under 6,4 x 10 rolling contacts under constant contact force and a probability of survival (i.e. avoiding cracks, pitting, excessive wear) of 90 % . For a wheel one revolution is equivalent to one rolling contact, whereas for a selected point in the rail the passing over of any wheel represents one rolling contact. In cases where the wheel is not rolling but the load is fluctuating, 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 Fu obtained from the equations in Table 5 shall be taken into account.

Fu is calculated separately for wheel and rail.

10

prCEN/TS 13001-3-3:2007 (E)

Table 5 — Minimum contact force

Fu related to the surface hardness of

Fu related to the yield point of the wheel

wheel or rail

or rail material

(5,2 ⋅ HB )

* 3

Point contact

(

)

3 2 § π · ª 3 ⋅ 1− v º ⋅¨ ¸ ⋅ « » © 1,5 ¹ ¬« Em ⋅ D2w + r1k »¼

(

(3,0 ⋅ HB )

* 2

Line contact

Fu

⋅

2

(1,6 ⋅ f )

3

)

y

π ⋅ Dw ⋅ b ⋅ (1 − v 2 )

(

(

(1,8 ⋅ f )

2

y

Em

)

3 2 § π · ª 3 ⋅ 1− v º ⋅¨ ¸ ⋅ « » © 1,5 ¹ ¬« Em ⋅ D2w + r1k »¼

⋅

2

)

π ⋅ Dw ⋅ b ⋅ (1 − v 2 ) Em

where

Em v

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

Dw

is the wheel diameter;

rk

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

HB ∗ fy b

6.3.3

is the equivalent elasticity modulus;

is the unit-conform hardness (see clause 0); is the yield point of the material at the depth of maximum shear (if surface hardened, before that process); is the load-bearing width (see Figure 2).

Contact force history parameter

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

s c = k c ⋅ vc

(10)

where

kc

is the contact force spectrum factor;

vc

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 S c 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

S c of contact force history parameter sc

Class

Sc 0

Sc 1

Sc 2

Sc 3

Sc 4

Sc 5

Sc 6

Sc 7

Sc 8

Sc 9

sc

0,008

0,016

0,032

0,063

0,125

0,25

0,5

1,0

2,0

4,0

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prCEN/TS 13001-3-3:2007 (E)

6.3.4

Contact force spectrum factor

The contact force spectrum factor

§F k c = 1/ i tot ⋅ ¦ ¨¨ Sd,f,i i =1 © FSd,f i tot

· ¸ ¸ ¹

k c is calculated by

m

(11)

where

i

is the index of one rolling contact with

FSd , f ,i ;

itot

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);

FSd,f,i

is the design contact force in contact i ;

FSd,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

vc =

vc is calculated by

itot iD

(12)

where

itot

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

iD

is the number of rolling contacts at reference point:

6.4

iD = 6,4 ⋅ 10 6 .

Factor of further influences

6.4.1

Basic formula

The factor

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

f f = f f1 ⋅ f f 2 ⋅ f f 3 ⋅ f f4 ⋅ f f 5 where

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

12

(13)

prCEN/TS 13001-3-3:2007 (E)

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 f f1 is set to 1. For the surface with the edge radius r3 (see Figure 2),

f f1 = f 1

(14)

where

f1 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 6.4.4

f f2 set to 1.

Skewing

A skewing wheel causes wear of wheel and rail and thus shortens the useful life. The wear is increased overproportionally in relation to the skewing angle α . This effect is taken into account by factor f f3 .

ff3 = 1 f f3 = 3

for

5

α

for

α≤

α>

0

5 /00

0

5 /00

(15)

where

α =α g +α w +α t

0

is the skewing angle of the crane in /00, calculated according to EN 13001-2.

The part of the skewing angle due to tolerances

αt

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

αt

1,5 /00

6.4.5

0

Tolerance class 2 0

2,5 /00

Tolerance class 3 0

3,5 /00

Tolerance class 4 0

4,5 /00

Matching materials

Wear and mechanical abrasion of wheel and rail depend considerably on the combination of mechanical properties (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 will increase wear of one partner and decrease wear of the other partner. This may be taken into account by factor f f4 . For a particular chosen pair of wheel and rail materials,

f f 4 shall be chosen such that:

13

prCEN/TS 13001-3-3:2007 (E)

f 4w =

1 f 4r

where

f f4 = f 4w

is the matching materials factor for a wheel,

f f 4 = f 4r

is the matching materials factor for a rail.

The factor f f 4 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 f f5 .

f f5 = 0,95 for driven wheels in unclean environment, f f5 = 1,0

14

for non-driven wheels or wheels in clean environment.

(17)

prCEN/TS 13001-3-3:2007 (E)

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

NO

Use 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 in reeving systems

prCEN/TS 13001-3-3:2007

Cranes — General design — Part 3-3: Limit states and proof of competence of wheel/ rail contacts

EN 13135-1:2003

Cranes — Safety – Design — Requirements for Equipment — Part 1: Electrotechnical equipment

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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prCEN/TS 13001-3-3:2007 (E)

Annex B (informative) Conversion table of hardness

Table B.1 — Conversion table of hardness Hardness HV

HBW

80

HRA

HRB

Hardness HRC

HRD

HV

HBW

HRA

HRC

HRD

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

16

HV

is the Vickers hardness;

HBW

is the Brinell hardness;

HR

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

prCEN/TS 13001-3-3:2007 (E)

Annex C (informative) Examples for matching materials factor

Table C.1 – Examples for matching materials factor

a

Material number wheel a (name)

Material number rail a (name)

f 4w

f 4r

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

1.7225 hardened and tempered (42CrMo4)

1.0624 (R0900Mn)

0,87

1,15

1.7229 hardened and tempered (61CrMo4)

1.0527 (C56)

1,25

0,8

1.7229 hardened and tempered (61CrMo4)

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

Numbers according to the “Register of European Steels”.

17

prCEN/TS 13001-3-3:2007 (E)

Bibliography

18

[1]

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

[2]

Hesse, W.: Verschleißverhalten des Laufrad-Schiene-Systems fördertechnischer Anlagen, Diss. RuhrUniversität 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, contact fatigue of railway wheels, Fatigue Fracture Engineering Materials and Structures 25 (2002), pages 899-909

[6]

EN 1990:2002, Eurocode, Basis of structural design