DIN 743-2-2012 Calculation of load capacity of shafts and axles - Part 2 Theoretical stress concentration factors and fatigue notch factors《轴和柄负载能力的计算 第2部分 理论应力集中因子和疲劳缺口因子》.pdf

1、December 2012 Translation by DIN-Sprachendienst.English price group 15No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).I

2、CS 21.120.10!%,d-“2096510www.din.deDDIN 743-2Calculation of load capacity of shafts and axles Part 2: Theoretical stress concentration factors and fatigue notchfactors,English translation of DIN 743-2:2012-12Tragfhigkeitsberechnung von Wellen und Achsen Teil 2: Formzahlen und Kerbwirkungszahlen,Engl

3、ische bersetzung von DIN 743-2:2012-12Calcul de la capacit des arbres et axes Partie 2: Coefficients thoriques de la concentration des contraintes, coefficients effectifsde la concentration des contraintes,Traduction anglaise de DIN 743-2:2012-12SupersedesDIN 743-2:2000-10www.beuth.deDocument compri

4、ses 34 pagesIn case of doubt, the German-language original shall be considered authoritative.08.15 DIN 743-2:2012-12 2 A comma is used as the decimal marker. Contents Page 1 Scope 5 2 Normative references 5 3 Symbols, designations and units .5 4 Fatigue notch factor 6 4.1 Definition of fatigue notch

5、 factor .6 4.2 Experimentally determined fatigue notch factors 6 4.2.1 Parallel keyway and interference fit .6 4.2.2 Fatigue notch factors for splined shafts, serrated shafts and involute spline shafts 8 4.2.3 Fatigue notch factors for round bars with V-notch . 10 4.2.4 Fatigue notch factors for cir

6、cumferential rectangular notch . 11 4.3 Fatigue notch factors for notches with known stress concentration factor 12 4.3.1 Shoulder, U-notch, shoulder with undercut, transverse hole 12 4.3.2 Notch cases not yet dealt with 14 5 Stress concentration factors . 14 5.1 Definition of stress concentration f

7、actor . 14 5.2 Stress concentration factors for different notch shapes . 15 5.2.1 Shoulder and U-notch 15 5.2.2 Shoulder with undercut 22 5.2.3 Transverse hole 23 6 Size influence factors . 24 6.1 General information 24 6.2 Technological size influence factor K1(deff) . 24 6.3 Geometrical size influ

8、ence factor K2(d) 26 6.4 Geometrical size influence factor K3(d) 27 7 Influence factor for surface roughness KF,. 28 8 Influence factor for surface conditioning KV. 30 Bibliography . 34 Figures Figure 1 Fatigue notch factors for splined shafts, serrated shafts and involute spline shafts . 8 Figure 2

9、 Fatigue notch factors for round bars with circumferential V-notch 2 10 Figure 3 Circumferential rectangular notch for circlips according to DIN 471 and structural radius * according to Neuber 9 . 11 Figure 4 Sensitivity factor n . 13 Figure 5 Stress concentration factors for notched round bars in t

10、ension . 16 Figure 6 Stress concentration factors for notched round bars in bending 17 Figure 7 Stress concentration factors for notched round bars in torsion 18 Figure 8 Stress concentration factors for shouldered round bars in tension 19 Figure 9 Stress concentration factors for shouldered round b

11、ars in bending . 20 Figure 10 Stress concentration factors for shouldered round bars in torsion 21 DIN 743-2:2012-12 3 Figure 11 Shoulder with undercut 22 Figure 12 Stress concentration factors for round bars with transverse hole in tension/ compression, bending or torsion (tension/compression 2, be

12、nding and torsion 1) 23 Figure 13 Technological size influence factor K1(deff) . 25 Figure 14 Geometrical size influence factor K2(d) 26 Figure 15 Geometrical size influence factor K3(d) 27 Figure 16 Influence factor for surface roughness KF. 29 Figure 17 Influence factor for surface conditioning, K

13、V, in chemico-thermal processes 31 Figure 18 Influence factor for surface conditioning, KV, in mechanical processes . 32 Figure 19 Influence factor for surface conditioning, KV, in thermal processes 32 Tables Table 1 Fatigue notch factors ,(dBK) for shaft-hub connections . 7 Table 2 Relative stress

14、gradient G . 14 Table 3 Stress concentration factor constants A, B, C and exponent z 15 Table 4 Influence factor for surface conditioning, KV, as a function of the technological process; guidance values 33 DIN 743-2:2012-12 4 Foreword This standard has been prepared by Working Committee NA 060-34-32

15、 AA Wellen- und Welle-Nabe-Verbindungen of Section Antriebstechnik of the Normenausschuss Maschinenbau (Mechanical Engineering Standards Commitee) in DIN. DIN 743, Calculation of load capacity of shafts and axles comprises Part 1: General Part 2: Theoretical stress concentration factors and fatigue

16、notch factors Part 3: Strength of materials Part 4: Fatigue limit, endurance limit Equivalently damaging continuous stress Supplement 1: Examples to part 1 to 3 Supplement 2: Examples to part 4 Amendments This standard differs from DIN 743-1:2000-10 as follows: a) Subclause 5.2 The paragraph titled

17、“Shoulder with undercut” has been revised. The superposition of two notch shapes (shoulder, U-notch) has been dropped. b) Clause 6 The decrease in the technological size influence factor for case hardened steels (except for Cr-Ni-Mo case hardened steels) with increasing diameter deffhas been limited

18、 to deff= 150 mm. The information about the decrease in the technological size influence factor for the yield strength of tempering steels has been added; c) Editorial changes have been made. Previous editions DIN 743-2: 2000-10 DIN 743-2:2012-12 5 1 Scope This standard determines the size influence

19、 factors, surface factors, stress concentration factors, or fatigue notch factors necessary for the calculation of the component fatigue strength according to DIN 743-1 (for more information see 11). If users have their own results or findings, they can use those quantities or factors for the calcul

20、ation in place of the factors stated in this standard. The given stress concentration factors and fatigue notch factors apply to solid shafts or hollow shafts with wall thicknesses where the bore does not yet have an influence on the notch. For circumferential notches the condition (D-di)/(2t) 3 ser

21、ves as orientation (see Annex A to DIN 743-1*). 2 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

22、 amendments) applies. DIN 471, Retaining rings for shafts Normal type and heavy type DIN 743-1, Calculation of load capacity of shafts and axles Part 1: Introduction, basic principles DIN 743-3, Calculation of load capacity of shafts and axles Part 3: Mechanical strength properties of materials DIN

23、6892, Drive type fastenings without taper action Parallel keys Calculation and design DIN 7190, Interference fits Calculation and design rules 3 Symbols, designations and units Symbol Designation Unit d Component diameter at notch cross section mm D Component diameter at shaft shoulder mm dBReferenc

24、e diameter mm dBKNotch reference diameter mm deffDiameter relevant for heat treatment mm diInside diameter (bore diameter) mm r Notch radius mm t Notch depth F Force N MbBending moment Nm MtTorsional moment Nm RzBMean roughness of test bar m a,Stress concentration factor ,Fatigue notch factor *,Auxi

25、liary value for fatigue notch factor maxKDecisive local principal stress at notch cross section N/mm2maxKDecisive local torsional stress (principal shear stress) at notch cross section N/mm2n, nNominal stress at notch cross section N/mm2zd,bW(d), tW(d) Fatigue limit of unnotched, polished round test

26、 bar of diameter d under reversed stress N/mm2*)Translators note. In German original: “DIN 743-1:2010”. DIN 743-2:2012-12 6 4 Fatigue notch factor 4.1 Definition of fatigue notch factor The fatigue notch factor of the component is defined by Equations (1) and (2): (1) (2) where zd,bWK, tWKare fatigu

27、e limits under reversed stress of the component with diameter d at notch cross section (expressed in nominal stress) zd,bW(d),tW(d) are fatigue limits under reversed stress of the unnotched, polished round test bar with diameter d under otherwise identical conditions. The fatigue notch factor for te

28、nsion/compression, bending or torsion can be calculated or determined experimentally, depending on the circumstances. 4.2 Experimentally determined fatigue notch factors The fatigue notch factors for the notch cases below were determined experimentally for defined test bar diameters only (dBK), (dBK

29、) for reference diameter dBK). The fatigue notch factor for component diameter d shall be calculated using Equation (3): (3) where K3(d), K3(dBK) are geometrical size influence factors (see Figure 15). Equation (3) applies to tension/compression or bending, but also to torsion, if is replaced by . F

30、or special components the fatigue notch factors shall be determined experimentally. 4.2.1 Parallel keyway and interference fit For the most common shaft-hub connections used in practice the fatigue notch factors can be taken from Table 1. DIN 743-2:2012-12 7 Table 1 Fatigue notch factors ,(dBK) for

31、shaft-hub connections Shaft and hub shape B(d) in N/mm2400 500 600 700 800 900 1000 1100 1200 (dBK) 2,1 a2,3 a2,5 a2,6 a2,8 a2,9 a3,0 a3,1 a3,2 a( ) ( )( )38,02/0001/0,3 mmNddBBK (dBK) 1,3 1,4 1,5 1,6 1,7 1,8 1,8 1,9 2,0 (dBK) 0,56 (dBK) + 0,1 In the case of two parallel keys, the fatigue notch fact

32、or ,shall be increased by factor 1,15 (reduction of cross section) (two parallel keys)= 1,15 (dBK) 1,8 2,0 2,2 2,3 2,5 2,6 2,7 2,8 2,9 ( ) ( )( )43,02/0001/7,2 mmNddBBK (dBK) 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,8 1,9 (dBK) 0,65 (dBK) The fatigue notch factor for the shoulder (transitional area between d a

33、nd d1) shall be determined according to 4.3. A ratio of diameters of d1/(1,1 d) is to be assumed for the determination of the stress concentration factor. In general, the interference fit only slightly influences the notch effect of the shaft shoulder fillet. Only in cases of unfavourable design mig

34、ht there be mutual influence as a result of the notch effect at the shaft shoulder fillet (radius r) and the hub fit. This can occur with very slight differences between d1and d and with shaft shoulder fillets directly contacting the end of the hub fit. Where calculated safety factors are low and th

35、e system is very important, the service life of the shaft shall then be separately checked (e.g. by means of FEM or experimentally; see also 7). With regard to the minimum total volume of the shaft at the shaft-hub connection, the dimensions for maximum load carrying ability are d/d1 1,1 and r/(d -

36、d1) 2 10. For more information about fatigue notch factors and influences, see DIN 7190. Nominal stresses: Reference diameter dBK= 40 mm Tension: n= 4F / (d2) Influence factor for surface roughness: KF= 1 or KF= 1 Bending: n= 32Mb/ ( d3) Bending or torsional moment is transmitted to the hub. Torsion

37、: n= 16Mt/ ( d3) The fatigue notch factors apply to the ends of the hub fit. The same values apply to tension/compression as to bending. aThe given ,values are approximate values. They contain influences resulting in deviations in the load carrying ability depending on the fit, the ratio of tm/ba,th

38、e heat treatment, and the dimensions of the hub. Interference between shaft and hub increases the load capacity. With tm/ba 0,5 the load carrying ability increases since, because of the parallel key, the friction caused by torsion in the parting line reduces the active bending moment in the shaft-hu

39、b connection (which was proven by experiment for steels without a hard surface). With mere rotational bending (tm/ba= 0), however, it is possible to reduce the load capacity by a factor of 1,3. Depending on the service life, the load capacity of parallel key connections can steadily decrease due to

40、tribocorrosion. For more information about fatigue notch factors and influences, see DIN 6892. DIN 743-2:2012-12 8 4.2.2 Fatigue notch factors for splined shafts, serrated shafts and involute spline shafts The fatigue notch factors for splined shafts, serrated shafts and involute spline shafts in to

41、rsion and bending can be approximately read from Figure 1 or calculated using the equations given below Figure 1. With relatively rigid hub and unfavourable design the fatigue notch factors can be considerably higher because of the load concentration in the shaft-hub transitional area. The values ap

42、ply to the shaft without influence by the hub. B(d) K1(deff) B(dB) in N/mm2Key 1 Splined shafts and serrated shafts 2 Involute spline shafts Figure 1 Fatigue notch factors for splined shafts, serrated shafts and involute spline shafts DIN 743-2:2012-12 9 Reference diameter dBK= 29 mm Fatigue notch f

43、actors 272()*( ) exp 4,2 10/BBKddN mm= Torsion: Splined shafts and serrated shafts: (dBK) = *(dBK) Involute spline shafts: (dBK) = 1 + 0,75 (*(dBK) 1) Bending: Splined shafts (dBK) = 1 + 0,45 (*(dBK) 1) Serrated shafts (dBK) = 1 + 0,65 (*(dBK) 1) Involute spline shafts: (dBK) = 1 + 0,49 (*(dBK) 1) T

44、ension/compression: The values for tension/compression are approximately the same as those for bending. Influence factor for surface roughness: KF= 1 or KF= 1 Case hardened steels: (dBK) = 1,0; (dBK) = 1,0; KV= 1 Nominal stresses: Torsion: n= 16 Mt/( d3) Bending: n= 32 Mb/( d3) DIN 743-2:2012-12 10

45、4.2.3 Fatigue notch factors for round bars with V-notch The fatigue notch factors for round bars with circumferential V-notch in tension/compression, bending or torsion are to be read from Figure 2 or calculated using the equation below Figure 2. B(d) K1(deff) B(dB) in N/mm2Key 1 Tension/compression

46、 2 Bending Figure 2 Fatigue notch factors for round bars with circumferential V-notch 2 Reference diameter: dBK= 15 mm Fatigue notch factors: Tension/compression: ( )( )20,109 1,074100 /BBKddN mm =+Bending: ( )( )20,0923 0,985100 /BBKddN mm =+Torsion: ( ) ( )BKBendingBK0,80 dd = DIN 743-2:2012-12 11

47、 Nominal stresses: Tension/compression: n= 4 F/( d2) Bending: n= 32 Mb/( d3) Torsion: n= 16 Mt/( d3) Radius in the notch root: r = 0,1 mm Mean roughness of notch: RzB= 20 m t/d = 0,05 up to 0,20; for other values, the fatigue notch factors deviate from this information. 4.2.4 Fatigue notch factors for circumferential rectangular notch The equations for the calculation of the fatigue notch factors for the notch shape “rectangular notch” are given below Figure 3 (methods according to 3, 4, 5, 6, 8). ( ) ( ) ( )eff1BSS