DIN 743 B1-2000(English version)Shafts and axles, calculation of load capacity

DIN 743 B1-2000(English version)Shafts and axles, calculation of load capacity DIN 743 (supplementary sheet) Content Page Foreword . . . . . . . . . . . . . . . . 2 1 Scope . . . . . . . . . . . . . . . 2 2 Normative references . . . . . . . . . . . . . 2 3 Symbols, Definitions and Units . . . . . . . . . . 2 4 Application example . . . . . . . . . . . . . 2 4.1 Proof against fatigue fracture and permanent deformation of stepped shafts under bending and torsion . . . . . . . . . . . . 2 4.2 Proof against fatigue fracture and permanent deformation of shafts with feather key slot under bending and torsion . . . . . . . 4 4.3 Proof against fatigue fracture and permanent deformation of axles with feather key slot under bending . . . . . . . . . . . 6 Foreword: The German standard DIN 743 has been prepared by the German institute for standardisation and the Institut für Maschinenelemente und Maschinenkonstruktion of the technical university of Dresden, Germany. The standard consists of 4 of parts: - Part 1: “Introduction, Basics” - Part 2: “Stress concentration factors and fatigue notch factors” - Part 3: “Material strength value” - Supplementary sheet 1: “Application examples” 1 Scope This standard comprises application examples for proof against fatigue strength according to DIN 743-1, 743-2 and 743-3. 2 Normative references DIN 743-1 DIN 743-2 DIN 743-3 3 Symbols, Definitions and Units Symbol Definition Unit d Diameter d mm dDatum diametermm B dNotch datum diameter mm BK n Number describing how far the material counteracts the stress concentration and lowers damage. r Notch radius mm 1 -1 GReferenced stress gradient mm 24 H Auxiliary quantity (for negative stresses) N/mm K σ,τ KStatic support coefficient 2F K,KSurface roughness factor FσFτ KSurface hardening factor V K(d) Technological size coefficient 1 K(d) Geometrical size coefficient 2 K(d) Geometrical size coefficient 3 MBending moment Nm b RAverage roughness μm Z S Actual safety T Torsional moment Nm α,αStress concentration factor στ β,βFatigue notch factor for compression/tension, bending στ and torsion 2σ,τMaterial fatigue strength for reference diameter N/mm zd.bWtW 2σ,τ Component fatigue strength N/mm zd.bWKtWK2σ,τ Permissible stress amplitudes, strengths N/mm zd.bADKtADK2σ,τ N/mm zd.bODKtODK2σ,τ Mean stress N/mm mm2σ,τ Stress amplitudes N/mm ata2σ,τ Maximum stress N/mm oo2σ,τ Minimum stress N/mm uu2 σ,τ Yield strength N/mmzd,bFKtFK2ψ,ψMean stress sensitivity N/mm σKτK γcoefficient for increasing the yield strength due to a F multi-axial stress state in a notch 2σ;(R) Tensile strength N/mm Bm2σ;(R,R) Component yield strength N/mm sp0.2e2σ Bending yield strength N/mm bF2τ Torsional yield strength N/mm tF Indices: A Permissible stress amplitude a Actual stress amplitude b Bending- bW Bending fatigue- D Fatigue strength K Notched component max Maximum- t, τ Torsion v Reference/equivalent- W Fatigue- 4 Application example 4.1 Proof against fatigue fracture and permanent deformation of stepped shafts under bending and torsion This example merely serves for demonstrating the calculation process. Known: Dimensions: D = 50 mm d = 42 mm r = 5 mm t = 4 mm Load (section cross at d): Material: 34CrMo4 (strength values according to DIN 743-3, d ? 16 mm): B Surface roughness: R= 5 μm Z Unknown: Safety of proof against fatigue fracture under type of load 1 and against exceeding of the yield strength. Calculation: (calculation scheme see DIN 743-1 Annex B). The calculation is made with notch and stress concentration factors according to DIN 743-2. a) Overall influence coefficient for bending - Stress concentration factor αaccording to image 9 of DIN 743-2 with σ d/D = 0.84; r/t = 1.25; r/d = 0.119; α = 1.557 σ - Stress gradient G’ according to table 2 in DIN 743-2 with υ = 0.179; G’ = -10.542 mm - Technological size coefficient K(d) (see page 6) according to equation 1eff (14) or image 13 in DIN 743-2 with d = 16 mm and d = 50 mm Beff - Coefficient n according to equation (5) or image 4 of DIN 743-2 with - Fatigue notch factor β according to equation (4) in DIN 743-2. σ - Geometrical size coefficient K(d) according to equation (17) or image 13 2 in DIN 743-2. - Surface roughness factor K according to equation (19) or image 14 of Fσ2DIN 743-2 with σ(d), σ(d) = σ(d)*K(d) = 871N/mm BBBB1eff - Surface hardening factor K = 1 V - Overall influence coefficient K according to equation (8) in DIN 743-1:σ b) Overall influence coefficient for torsion - Stress concentration factor αaccording to image 10 of DIN 743-2 with τ d/D = 0.84; r/t = 1.25; r/d = 0.119; α = 1.283 τ - Stress gradient G’ according to table 2 in DIN 743-2 with υ = 0.179; G’ = -10.23 mm - Technological size coefficient K(d) (see page 6) according to equation 1eff (14) or image 13 in DIN 743-2 with d = 16 mm. B - Coefficient n according to equation (5) or image 4 of DIN 743-2 with - Fatigue notch factor β according to equation (4) in DIN 743-2. τ - Geometrical size coefficient K(d) according to equation (17) or image 13 2 in DIN 743-2. - Surface roughness factor K according to equation (20) or image 14 of Fτ DIN 743-2 - Surface hardening factor K = 1 V - Overall influence coefficient K according to equation (9) in DIN 743-1: τ c) Safety for proof against fatigue fracture according to type of load 1. - Average reference stress according to equations (23) and (24) in DIN 743-1 - component fatigue strength σ, τ according to equations (6) and (7) WKWK in DIN 743-1 - Average stress sensitivity ψ,ψ according to equations (21) and (22) in σKτK DIN 743-1 - Safety S according to equation (2) in DIN 743-1 d) Safety for proof against exceeding of the yield strength. - Static support coefficient K for bending and torsion according to table 3 2F in DIN 743-1 - γ according to table 2 in DIN 743-1 F - component yield strength σ, τ according to equation (28) and (29) in bFKtFK DIN 743-1 with K(d) = 0.871. 1eff - Safety S according equation (25) in DIN 743-1 The proof against exceeding of the yield strength defines the diameter of the component. 4.2 Proof against fatigue fracture and permanent deformation of shafts with feather key slot under bending and torsion Known: d = 50 mm Load: Changing bending moment: M = +/- 1200Nm b Static torsional moment: T = 3000 Nm Impact loading: M = 1.5*M ; T = 1.5*T bmaxbmax Material: 34CrMo4 (strength values according to DIN 743-3, d ? 16 mm): B Surface roughness: R= 12.5 μm Z Unknown: Safety of proof against fatigue fracture under type of load 1 and against exceeding of the yield strength. Calculation: (calculation scheme see DIN 743-1 Annex B). The calculation is made with experimentally determined notch factors according to DIN 743-2. a.) Overall influence coefficient for bending - Technological size coefficient K(d) according to equation (14) or 1eff image 13 in DIN 743-2 with d = 16 mm and d = 50 mm Beff - Fatigue notch factor for datum diameter d = 40 mm according to table BK 1 in DIN 743-2 with σ(d) = σ (16 mm) * K(d = 50 mm) = 958,1 BBB1eff2N/mm; β(d)= 2,95 σBK - Geometrical size coefficient K(d) and K(d) according to equation (18) 33B or image 13 in DIN 743-2 - Fatigue notch factor β for part diameter d according to equation (3) in σ DIN 743-2 - Geometrical size coefficient K(d) according to equation (17) or image 13 2 in DIN 743-2 - Surface roughness factor K according to table 1 in DIN 743-2. K = 1. FσFσ - Surface hardening factor K = 1 V - Overall influence coefficient K according to equation (8) in DIN 743-1 σ b.) Load (nominal stress referred to the gross section): - Bending stress amplitude σ: ba - Average torsional stress: c.) Safety of proof against fatigue strength under type of load 1: - Average reference stress according to equation (23) in DIN 743-1 - Component fatigue strength σ according to equation (6) in DIN 743-1bWK - Average stress sensitivity ψ according to equation (21) in DIN 743-1σK - Stress amplitude of the part fatigue strength σ according to equation bADK (11) in DIN 743-1. - Safety S according to equation (3) in DIN 743-1 d.) Safety S of proof against exceeding of yield strength - Static support coefficient K for bending and torsion according to table 2F 3in DIN 743-1 - Increasing of the yield strength γ according to table 2 in DIN 743-1: F (no circumferential groove) - part yield strength σ, τ according to equations (28) and (29) in DIN bFKtFK 743-1 with K(d) = 0.871 1eff 2- Safety S according to equation (25) in DIN 743-1; σ = 146.7 N/mmbmax - The fatigue strength defines the part diameter. 4.3 Proof against fatigue fracture and permanent deformation of axles with feather key slot under bending Known: D = 122 mm D = 80 mm 1 d = 79.4 mm t = 21.3 mm r = 0.8 mm Load: M = M +/- M = 8000 Nm +/- 2500 Nm bbmba Material: E335 (constructional steel, strength values according to DIN 743-3 d = 16 mm) B22σ = 590 N/mm; σ= 590 N/mm BS 22σ= 235 N/mm; σ = 290 N/mm zdW bW2τ = 180 N/mm tW Surface roughness: R = 25 μm Z Unknown: Safety of proof against fatigue fracture under type of load 2 and against exceeding of the yield strength. Calculation: (calculation scheme see DIN 743-1 Annex B). The calculation is made with notch factors of notches with known stress concentration factors according to DIN 743-2. a.) Overall influence coefficient - Stress concentration coefficients according to table 3 in DIN 743-2 C-slot: A = 0.2, B = 2.75 Step: A = 0.62, B = 5.8, C = 0.2, z = 3 - stress concentration factor α according to equations (9) and (11) in DIN σ 743-2 = 0 (step, d/D - stress gradient G’ according to table 2 in DIN 743-2 with υ < 0.67 => υ = 0) - Technological size coefficient K(d) according to equations (12) and 1eff (13) in DIN 743-2 with d = 16 mm and d= 12 mm. Beff tensile strength: K(d) = 1 1eff yield strength: - n according to equation (5) or image 4 in DIN 743-2 with σ(d) = S2σ(d)*K(d) = 284.4 N/mm SB1eff - Notch factor β according to equation (4) in DIN 743-2 with α = α = σσσF 3.791 - Geometrical size coefficient K(d) according to equation (17) or image 13 2 in DIN 743-2 with K(d) = 1 1eff - Surface hardening coefficient K = 1 V - Surface roughness factor K according to equation (19) or image 14 in Fσ2DIN 743-2 with K(d) = 1 and σ = 590 N/mm. 1effB - Overall influence factor K according to equation (8) in DIN 743-1: σ b.) Load - Average bending stress σ: bm - Bending stress amplitude σ: ba - Maximum bending stress σ: bmax c.) Safety of proof against fatigue fracture under type of load 2 2- Average reference stress σ = σ = 162.8 N/mm mvbm2- Upper reference stress σ = σ = 213.7 N/mm vobo2- Lower reference stress σ = σ - σ = 111.9 N/mm vubmba - Component fatigue strength σ according to equation (6) in DIN 743-1 bWK with K(d) = 1 1eff - Stress amplitude of the component fatigue strength σ according to bADK equation (16) in DIN 743-1 - Safety S according to equation (3) in DIN 743-1 d.) Safety S of proof against exceeding of yield strength - Static support coefficient K according to table 3 in DIN 743-1: Bending: 2F K = 1.2 2F - Increasing of the yield strength γ according to table 2 in DIN 743-1: F (no circumferential notch) - part yield strength σ, τ according to equations (28) and (29) in DIN bFKtFK 743-1 with K(d) = 0.871 1eff 2- Safety S according to equation (25) in DIN 743-1; σ = 146.7 N/mm; bmax2τ = 183.3 N/mm tmax - The fatigue strength defines the part diameter.