EN 13001-3-3

ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɋɌȺɇȾȺɊɌɊȿɋɉɍȻɅɂɄɂ 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 ɉɪɟɞɟɥɶɧɵɟ ɫɨɫɬɨɹɧɢɹ ɢ ɩɨɞɬɜɟɪɠɞɟɧɢɟ ɛɟɡɨɩɚɫɧɨɫɬɢ ɤɨɥɟɫɧɵɯ ɢ ɪɟɥɶɫɨɜɵɯ ɤɨɧɬɚɤɬɨɜ ɄɊȺɇɕ ȺȽɍɅɖɇȺə ɄȺɇɋɌɊɍɄɐɕə ɑɚɫɬɤɚ 3-3. ɤɚɤ ɫɬɚɧɞɚɪɬ.Ⱥ). ȼɜɟɞɟɧ ɜ ɞɟɣɫɬɜɢɟ. Limit states and proof of competence of wheel/rail contacts Ⱦɚɬɚ ɜɜɟɞɟɧɢɹ 2010-01-01 III . ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɋɌȺɇȾȺɊɌ ɊȿɋɉɍȻɅɂɄɂ ȻȿɅȺɊɍɋɖ ɄɊȺɇɕ ɈȻɓȺə ɄɈɇɋɌɊɍɄɐɂə ɑɚɫɬɶ 3-3. ɧɚ ɤɨɬɨɪɵɣ ɟɫɬɶ ɫɫɵɥɤɚ ɜ ȿɜɪɨɤɨɞɟ EN 1993-6:2005. Ƚɪɚɧɿɱɧɵɹ ɫɬɚɧɵ ɿ ɩɚɰɜɹɪɞɠɷɧɧɟ ɛɹɫɩɟɤɿ ɤɨɥɚɜɵɯ ɿ ɪɷɣɤɚɜɵɯ ɤɚɧɬɚɤɬɚʆ Cranes General design Part 3-3.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. the unitconform hardness is given by HB * = HBW ⋅ N mm 2 (1) where * HB is the unit-conform Hardness. This Technical Specification is applicable to cranes that are manufactured after the date of approval by CEN of this standard.1 Terms. Cranes — vocabulary — Part 1: General ISO 12488-1. For dated references. 1 . EN 1991-1:1994 and Clause 6 of ISO 4306-1:1990. the latest edition of the referenced document (including any amendments) applies. 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. methodology (ISO 12100-1:2003) ISO 4306-1:1990. Normative references The following referenced documents are indispensable for the application of this document. EN 13001-1. Cranes — General Design — Part 2: Load actions EN ISO 6506-1. 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. the terms and definitions given in EN ISO 12100-1:2003.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. Cranes — General Design — Part 1: General principles and requirements EN 13001-2. 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. definitions. Cranes — Tolerances for wheels and travel and traversing tracks — Part 1: General 3 3. Metallic materials — Brinell hardness test — Part 1: Test method (ISO 6506-1:2005) EN ISO 12100-1:2003. only the edition cited applies. requirements and methods to prevent mechanical hazards of wheel/rail contacts of cranes by design and theoretical verification. general principles for design — Part 1: Basic terminology. Safety of machinery — Basic concepts. symbols and abbreviations Terms and definitions For the purposes of this Technical Specification. NOTE 2 CEN/TS 13001-3-3 deals only with limit state method according to EN 13001-1. For undated references. and serves as reference base for the Technical Specifications for particular crane types. This standard covers steel and cast iron wheels. Using SI-units. The unit of HB* has to match with the unit of the modulus of elasticity used in the calculation. 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.s Limit design contact force FSd.prCEN/TS 13001-3-3:2007 (E) HBW EXAMPLE NOTE 3. A Brinell hardness HB of 300 results into a unit-conform hardness HB* = 300 N/mm². Annex B provides a table of hardness conversion. the symbols and abbreviations given in Table 1 apply.f Design contact force for fatigue FSd.2 is the value of the Brinell hardness. Symbols and abbreviations For the purposes of this Technical Specification. f 4r 2 Description Matching materials factor for wheel or rail in fatigue .f Limit design contact force for fatigue FRd.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.i Design contact force in contact FSd. Both constitute the contact force history parameter sc (see 6. f. 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. 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. 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.1 γn Risk coefficient γp Partial safety factors v Radial strain coefficient ( v = 0. It is independent of time. 3 . abbreviations HBW Brinell Hardness HB * Unit-conform hardness HR * Rockwell hardness HV * Vickers hardness i Index of one rolling contact with FSd.3.3). The contact force history parameter is used for the selection of wheels and rails.3 for steel) vc Relative total number of rolling contacts φ Dynamic factors (see EN 13001-2) General In all cranes.prCEN/TS 13001-3-3:2007 (E) Table 1 (continued) Symbols. γ m = 1.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 . 5. edge effects).3 Static limit design contact force 5.2 FSd.02 % of the wheel radius. ⎯ decreasing effects (stiffness.s of all wheel/rail contacts shall be calculated for all relevant load combinations of EN 13001-2.1 General A contact force of the magnitude of the static limit design contact force FRd.3. 5 Proof of static strength 5. 5. 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.3.s causes permanent radial deformation of 0. The static limit design contact force FRd.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 . FRd.s s the limit design contact force. ⎯ geometry (radii of wheel and rail). ⎯ contact case (point contact or line contact). taking into account the respective dynamic factors φ.s (2) where 5.s depends on: ⎯ materials properties (modulus of elasticity and hardness) of wheel and rail. This standard is for design purposes only and should not be seen as a guarantee of actual performance. Design contact force The design contact force FSd. NOTE 2 This standard is applicable for metallic wheel/rail contacts only. Other materials require the applicability of the Hertz theory of contact pressure.s ≤ FRd.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.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. partial safety factors γp and where required the risk coefficient γ n .s is the design contact force. 5.4 Point contact Formula (4) gives the static limit design contact force shear is situated at depth FRd. (In case Er is the modulus of elasticity of the rail. E w is the modulus of elasticity of the wheel.3. * If the hardness of wheel and rail are different.s for cases of point contact the point of maximum Z mp below the surface.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.3. the lower value shall be taken. Typical point contacts are shown in Figure 1. material of rail 5. Ew = Er then of course Em = E w = Er ) Values of the elastic modules for selected materials are given in Table 2.prCEN/TS 13001-3-3:2007 (E) Em = 2 ⋅ E w ⋅ Er E w + Er (3) where Em is the equivalent modulus of elasticity . Table 2 — Values of elastic modules for selected materials Material of wheel. 5 . For hardened materials it shall be ensured that the hardness assumed in calculations reaches deeper into the material than the point of maximum shear. v is the radial strain coefficient ( v = 0.s = 1 γm zmp = 4.7 ⋅ (10 HB ) * 3 ( ) 3 2 § π · ª 3 ⋅ 1− v º ⋅¨ ¸ ⋅ « » © 1. HB ∗ is the unit-conform hardness (see chapter 0) at the point of maximum shear. rk is the radius of the rail surface or the second wheel radius (see Figure 1).prCEN/TS 13001-3-3:2007 (E) Key FRd.5 ¹ ¬« Em ⋅ D2w + r1k ¼» ( ( HB * 2 ⋅ π ⋅ 1 − ν 2 ⋅ γ m Em ⋅ D2w + r1k ( 2 ) ) ) (4) (5) where FRd.1 Line contact General Formula 6 gives the static limit design contact force shear is situated at depth Z ml below the surface. Dw is the wheel diameter. z mp is the depth of point of maximum shear. γm is the general resistance coefficient.3 for steel). The point of maximum .5 5.3.s for cases of line contact.3. γ m =1.5. 6 FRd. Em is the equivalent elasticity modulus.1. Figure 1 — Point contact 5.s is the static limit design contact force for point contact. Dw is the wheel diameter. f2 is the decreasing factor for non-uniform pressure distribution. b is the load-bearing width (see Figure 2). z ml is the depth of point of maximum shear.s is the static limit design contact force for line contact.3 for steel ). Em is the mean modulus of elasticity. HB ∗ is the unit-conform hardness (see chapter 0) at the point of maximum shear. f1 is the decreasing factor for edge pressure. γm is the general resistance coefficient.s = 1 γm z ml = 7.1. Figure 2 — Line contact 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.prCEN/TS 13001-3-3:2007 (E) Typical line contacts are shown in Figure 2. v is the radial strain coefficient ( v = 0. γ m =1. Key FRd. 1< r3 / w < 0. This effect is taken into account by factor f 2 .0 0.75 0. bending of main girders) or tolerances in rail alignment result in non-uniform pressure distribution. Figure 3 — Edge pressure Table 3 — Factor edge f1 for edge pressure r3 / w f1 r3 / w ≤ 0.8 [0. 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 1.25 (r3 / w)]/ 0.2 Edge pressure Sharp edges at the end of the contact line of wheel or rail decrease the limit design contact force. 5.prCEN/TS 13001-3-3:2007 (E) 5.0 1.5.1 0. given in Table 4 (Tolerance classes according ISO 12488-1). Otherwise deformation of the crane structure (e.6 . decreasing the limit design contact force.g.3.0 where w is the width of the projecting non-contact area and r3 is the radius of the edge.5 + 0.95 0.8 0.85 0.5.75 0.3 Pressure distribution An ideal uniform distribution requires sufficient elasticity of the rail fixation or support and/or wheels in hinged legs.9 0.7 0. This effect is taken into account by factor f1 .8 0.9 0.7 0.7 r3 / w ≥ 0. given in Table 3.8 1.3. 9 .prCEN/TS 13001-3-3:2007 (E) 6 Proof of fatigue strength 6.f is the design contact force for fatigue. m is the exponent for wheel/rail contacts.1.f is the limit design contact force for fatigue. γ cf = 1.1 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. partial safety factors γp.f shall be calculated for wheels and rails separately by ⋅ ff (9) where Fu is the minimum contact force. m = 3 for cases of point contact and m = 10/3 for cases of line contact.3 Limit design contact force 6.f (8) where 6.f = Fu m s c ⋅ γ cf FRd.f ≤ FRd.2 FSd. γ cf is the minimum contact resistance factor. and risk coefficient γn set to 1.3. ff is the factor of further influences. sc is the contact force history parameter.1 Basic formula The limit design contact force FRd.f shall be calculated for regular loads (load combinations A of EN 13001-2). The skewing forces acting on guide rollers shall be considered as regular loads. 6. with the respective dynamic factors φ . FRd. Design contact force The design contact force FSd. In cases where the wheel is not rolling but the load is fluctuating. avoiding cracks.3.prCEN/TS 13001-3-3:2007 (E) 6. whereas for a selected point in the rail the passing over of any wheel represents one rolling contact. one load cycle shall be considered as one rolling contact.4 x 10 rolling contacts under constant contact force and a probability of survival (i. excessive wear) of 90 % . 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. pitting.e. The minimum contact force for wheel/rail is dependent upon either the surface hardness or on the yield point as given in Table 5. 10 .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. For a wheel one revolution is equivalent to one rolling contact. then in formula (9) the exponent m shall be set to 3.6 ⋅ f ) 3 ) y π ⋅ Dw ⋅ b ⋅ (1 − v 2 ) ( ( (1.016 0. rk is the radius of the rail surface or the second wheel radius (see Figure 1). Contact force history parameter In analogy to stress history parameter (see EN 13001-1).0 11 .0 2.2 ⋅ HB ) * 3 Point contact ( ) 3 2 § π · ª 3 ⋅ 1− v º ⋅¨ ¸ ⋅ « » © 1.3. is the load-bearing width (see Figure 2). Dw is the wheel diameter.3).063 0.5 ¹ ¬« Em ⋅ D2w + r1k »¼ ( (3.25 0. 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.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 (5.3 is the equivalent elasticity modulus.125 0. is the yield point of the material at the depth of maximum shear (if surface hardened. the contact force history parameter is given by s c = k c ⋅ vc (10) where kc is the contact force spectrum factor. 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 6.5 1.0 ⋅ HB ) * 2 Line contact Fu ⋅ 2 (1. before that process). is the unit-conform hardness (see clause 0).0 4. If Table 6 is used. HB ∗ fy b 6.8 ⋅ 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 = 0.008 0. vc is the relative total number of rolling contacts.032 0. independent of the contact case. i is the design contact force in contact i .i i =1 © FSd.6.f.4. iD is the number of rolling contacts at reference point: 6.prCEN/TS 13001-3-3:2007 (E) 6.4. m is the exponent for wheel/rail contacts.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. 12 (13) . 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.4 Contact force spectrum factor The contact force spectrum factor §F k c = 1/ i tot ⋅ ¦ ¨¨ Sd.i .4.4 iD = 6.f i tot · ¸ ¸ ¹ k c is calculated by m (11) where i is the index of one rolling contact with FSd .4 ⋅ 10 6 .3.3. FSd.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. Factor of further influences 6.f is the maximum design contact force.f.2 to 6. f . 6. 4. Matching materials cause equal wear of a wheel and a rail per rolling contact. This may be taken into account by factor f f4 .5 /00 Tolerance class 4 0 4.2. ultimate strength) of wheel and rail.4 f f2 set to 1. Skewing A skewing wheel causes wear of wheel and rail and thus shortens the useful life. 6. Table 7 — Alignment angle of single wheel or roller Alignment Tolerance class 1 αt 1.4.4. 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 /00.5 /00 Matching materials Wear and mechanical abrasion of wheel and rail depend considerably on the combination of mechanical properties (e.5.5 /00 Tolerance class 3 0 3.5 0 Tolerance class 2 0 2.g. type of material.4.prCEN/TS 13001-3-3:2007 (E) 6. For a particular chosen pair of wheel and rail materials. The part of the skewing angle due to tolerances αt shall be chosen according to the tolerance as given in Table 7.2 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 1.3. calculated according to EN 13001-2. Non-matching materials will increase wear of one partner and decrease wear of the other partner. The wear is increased overproportionally in relation to the skewing angle α . For the surface with the edge radius r3 (see Figure 2). This effect is taken into account by factor f f3 .5 /00 6. f f 4 shall be chosen such that: 13 . hardening. f f1 = f 1 (14) where f1 is the factor for edge pressure as given in 5.3 Pressure distribution For the proof of fatigue strength the pressure distribution may be neglected and 6. 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. 6.6 Mechanical drive factor In an unclean environment the mechanical abrasion effects on the driven wheels may be taken into account by factor f f5 .95 for driven wheels in unclean environment. Examples are given in informative Annex C. (17) . f f5 = 0.0 14 for non-driven wheels or wheels in clean environment. f f5 = 1. The factor f f 4 shall be chosen from experience in the range between 0.5.4.66 and 1. f f 4 = f 4r is the matching materials factor for a rail. 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 15 . 2 105 99.5 560 517 77.5 370 351. HRB.8 90 85.8 115 109.7 53.8 95 90.8 53.8 77 480 450 74.9 48.3 80.1 60. HBW is the Brinell hardness.7 61.7 360 342 68.7 36.7 49.5 58.9 85 80.prCEN/TS 13001-3-3:2007 (E) Annex B (informative) Conversion table of hardness Table B.5 85 530 492 76.3 45.1 — Conversion table of hardness Hardness HV HBW 80 HRA HRB Hardness HRC HRD HV HBW HRA HRC HRD 76 350 332.6 52.8 56.8 400 380 70.5 120 114 67 430 408.1 50.8 55.1 510 475 75.2 37.4 190 180.7 57.3 59. HRC.5 78.3 49.4 51.3 550 509 77 52.8 40.4 53 65.5 69.1 540 500 76.5 71.5 62 410 389.1 35.5 520 483 76.8 185 175.8 69 440 418 72.5 72 43.6 58.4 100 95 390 370. HRD.8 38.6 420 399 71.5 63.3 150 142.8 where 16 HV is the Vickers hardness. HR is the Rockwell hardness as follows HRA.8 62.5 51.8 83.7 145 137.8 54. .1 62.1 460 432 73.1 140 133 75.2 125 118.8 88.5 170 161.3 64.2 160 152 82.7 51.4 180 171 87.7 64.1 63.2 380 361 69.4 61.3 73.3 39.5 71 450 423 73.3 64.5 500 466 75.3 44.4 41.3 86.5 47.5 68.8 490 456 74.6 65.8 42.8 130 123.6 46.9 165 156.1 46.5 89.6 570 526 77.8 56 110 104.5 70.1 470 442 74.9 175 166.4 135 128.9 60.6 155 147. 77 1.7229 hardened (61CrMo4) 1.0624 (R0900Mn) 0.0558 (GS-60) 1.87 Numbers according to the “Register of European Steels”.0527 (C56) 1. 17 .87 1.25 0.0527 (C56) 1.6956 hardened (33NiCrMo14-5) 1.1 – Examples for matching materials factor a Material number wheel a (name) Material number rail a (name) f 4w f 4r 1.0624 (R0900Mn) 0.0527 (C56) 1.7225 hardened (42CrMo4) 1.5 0.0624 (R0900Mn) 1.0624 (R0900Mn) 1 1 1.50 0.95 1.0624 (R0900Mn) 1.7225 hardened and tempered (42CrMo4) 1.prCEN/TS 13001-3-3:2007 (E) Annex C (informative) Examples for matching materials factor Table C.15 0.0527 (C56) 1 1 1.7229 hardened and tempered (61CrMo4) 1.05 0.87 1.7229 hardened and tempered (61CrMo4) 1.7225 hardened and tempered (42CrMo4) 1.0527 (C56) 1.0558 (GS-60) 1.25 1.66 1.66 1.15 1.8 1.0624 (R0900Mn) 1.3 0.7225 hardened (42CrMo4) 1.6956 hardened (33NiCrMo14-5) 1.15 0.0527 (C56) 1 1 1.7229 hardened (61CrMo4) 1.8 1. pages 899-909 [6] EN 1990:2002. Springer Verlag Berlin. EKBERG.: Verschleißverhalten des Laufrad-Schiene-Systems fördertechnischer Anlagen. M. Eurocode. G.: Grundlagen der Fördertechnik — Elemente und Triebwerke. Fatigue Fracture Engineering Materials and Structures 25 (2002). contact fatigue of railway wheels.prCEN/TS 13001-3-3:2007 (E) Bibliography 18 [1] Niemann. KABO and H. CETIM. Diss. 1B2302 et 1B2303. J-F. E. [2] Hesse. RuhrUniversität Bochum 1983.: Maschinenelemente Band I. Basis of structural design . Auflage. Juin 2003 [5] A. ANDERSON — An engineering model for prediction of rolling. W. Vieweg Verlag 1994. 2. [3] Scheffler. [4] Calcul en fatigue du contact galet/rail. FLAVENOT.