DIN 743-4-2012 Calculation of load capacity of shafts and axles - Part 4 Fatigue limit endurance limit - Equivalently damaging continuous stress《轴和柄负载能力的计算 第4部分 疲劳极限、持久极限 等效破坏连续应力》.pdf

1、December 2012 Translation by DIN-Sprachendienst.English price group 8No 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).IC

2、S 21.120.10!%,d.“2096511www.din.deDDIN 743-4Calculation of load capacity of shafts and axles Part 4: Fatigue limit, endurance limit Equivalently damaging continuous stress,English translation of DIN 743-4:2012-12Tragfhigkeitsberechnung von Wellen und Achsen Teil 4: Zeitfestigkeit, Dauerfestigkeit Sc

3、hdigungsquivalente Spannungsamplitude,Englische bersetzung von DIN 743-4:2012-12Calcul de la capacit des arbres et axes Partie 4: Rsistance la fatigue pour une dure de vie limite, rsistance la fatigue pourunedure de vie illimite Amplitude de contrainte pour endommagement quivalent,Traduction anglais

4、e de DIN 743-4:2012-12www.beuth.deDocument comprises 11 pagesIn case of doubt, the German-language original shall be considered authoritative.08.15 DIN 743-4:2012-10 2 A comma is used as the decimal marker. Contents Page Foreword 3 1 Scope 4 2 Normative references 4 3 Symbols, designations and units

5、 .4 4 Calculation 5 4.1 General 5 4.2 Single direction of loading 5 4.2.1 Calculation of safety factor for time-constant amplitude in the limited life strength domain 5 4.2.2 Calculation of safety factor for load spectra in the limited life strength and fatigue strength domains .7 4.3 Combined loads

6、 10 Bibliography . 11 Figures Figure 1 Limited life strength value ANK6 Figure 2 Method according to Miner extended . 8 DIN 743-4:2012-10 3 Foreword This standard has been prepared by Working Committee NA 060-34-32 AA Wellen- und Welle-Nabe-Verbindungen of Section Antriebstechnik of the Normenaussch

7、uss Maschinenbau (Mechanical Engineering Standards Committee) in DIN. DIN 743, Calculation of load capacity of shafts and axles comprises: Part 1: General Part 2: Theoretical stress concentration factors and fatigue notch factors Part 3: Strength of materials Part 4: Fatigue limit, endurance limit -

8、 Equivalently damaging continuous stress Supplement 1: Examples to part 1 to 3 Supplement 2: Examples to part 4 DIN 743-4:2012-10 4 1 Scope This standard applies to the calculation and verification of the safety of shafts and axles, in accordance with DIN 743-1, in the limited life strength domain (

9、fatigue failure) as well as in the limited life strength and fatigue strength domains for load spectrum loading. Users can make use of their own verified experience or results. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated

10、 references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. DIN 743-1, Calculation of load capacity of shafts and axles Part 1: General 3 Symbols, designations and units Symbol Designation Unit DMMiner sum _ i

11、 Load bin of the load spectrum _ j Number of load spectrum bins _ KKLoad spectrum factor _ K Corrected number of load spectrum bins _ neCorrected number of load cycles in bin k _ ni Number of load cycles in bin i _ NDSalient point of the Whler curve between the limited life strength and fatigue stre

12、ngth domains _ NL Required number of load cycles _ N* Reference number of load cycles _ NSSalient point of the Whler curve between the quasi-static strength and the limited life strength domain _ q Exponent of the Whler curve _ S Safety of the component _ SminRequired minimum safety of the component

13、 _ n Shape of the load spectrum _ zd,bADK,ttADKFatigue strength value N/mm2zd,bANK,ttANKLimited life strength value N/mm2DIN 743-4:2012-10 5 zd,ba,ttaEquivalent damaging stress amplitude N/mm2zd,bai,ttaiStress amplitude of load bin i N/mm2zd,ba1,tta1 Maximum stress amplitude of the given load spectr

14、um N/mm2S,StSingle safety _ Subscripts b Bending t, Torsion zd Tension/compression Tension/compression, bending 4 Calculation 4.1 General The method described in this standard takes into account the complete load spectrum covering the number of load cycles before the salient point NDof the Whler cur

15、ve. The decrease in fatigue strength caused by higher effective loads has been considered by approximation. The influence of order is not taken into account. The assumptions on which the Whler curve is based apply for notched round bars. ADKshall be calculated in accordance with DIN 743-1. For cases

16、 where m= constant and/or tm= constant it shall be assumed that mand ttmhave a constant value in all bins of the load spectrum and in the case of load increases remain constant in all bins of the load spectrum; this condition accordingly applies to zd,ba/m= constant and/or a/m= constant, i.e. the re

17、lation of the stress amplitude to the mean stress is constant in all bins of the load spectrum. 4.2 Single direction of loading 4.2.1 Calculation of safety factor for time-constant amplitude in the limited life strength domain 4.2.1.1 Basic equations The safety values shall be calculated on the basi

18、s of the maximum endurable stress (strength) and the stress existing in the case of application. The calculated safety factor S shall be equal to or greater than the minimum safety factor Smin: Smin 1,2 (1) The principles of the calculation method itself require a minimum safety factor Smin= 1,2. Un

19、certainties in the assumed load, possible consequential damage, etc. require higher safety factors. They shall be agreed upon or determined by the designer, depending on the case of application. DIN 743-4:2012-10 6 4.2.1.2 Working stresses If a calculation is to be made in the limited life strength

20、domain without taking into consideration load spectra, the working stresses shall be determined according to DIN 743-1. If load spectra are to be taken into consideration, proceed as described in subclause 4.2.2 of this standard. 4.2.1.3 Limited life strength value Regarding the limited life strengt

21、h domain the Whler curve equation, which is used to convert fatigue strength to limited life strength, generally applies: ,Dqzd bANK zd bADKLNN= (2) where q is the exponent of the Whler curve for bending DqtANK tADKLNNttt= (3) where qtis the exponent of the Whler curve for torsion. Unless otherwise

22、specified or known by experience, for notched round bars q = 5 for bending or tension/compression and qt = 8 for torsion can be assumed. Equations (3) and (4) apply for NS NL ND. NSand NDare mainly dependent on S, q,t, ADand ,tor ,t. For the salient points of the Whler curve, ND= 106or NS= 103is ass

23、umed here (Figure 1). If other values are to be used they shall be set accordingly. Key 1 Limited life strength domain 2 Fatigue strength domain Figure 1 Limited life strength value ANKDIN 743-4:2012-10 7 4.2.2 Calculation of safety factor for load spectra in the limited life strength and fatigue st

24、rength domains 4.2.2.1 Basic equations When calculating a safety factor by taking into consideration the effect of load spectra, the calculation procedure according to DIN 743-1 is applied. Fatigue strength: S = zd,bADK/zd,baor S = tADK/ta(4) Limited life strength: S = zd,bANK/zd,baor S = tANK/ta(5)

25、 S SminThe principles of the calculation method itself require a minimum safety factor Smin= 1,2. Uncertainties with the assumed load, possible consequential damage, etc. require higher safety factors. They shall be agreed upon or otherwise determined. A progression of the Whler curve similar to Fig

26、ure 1 is prerequisite for the calculation method. NOTE Recent tests show that in the case of very high cycle fatigue (N 108) the fatigue strength can continue to taper off. This is mainly put down to the effect of micro inclusions. In some cases, fatigue strength also continuously tapers off with N

27、ND. This was found, for example, on through-hardened rolling bearing steels and under the influence of aggressive media. This tapering off of fatigue strength shall be taken into consideration separately. 4.2.2.2 Working stresses To maintain the method of proving the fatigue strength in accordance w

28、ith DIN 743-1, from the given load spectrum and the (nominal) stress spectrum that can be directly calculated from it, a constant equivalent damaging stress amplitude is determined by the method according to “Miner extended” (see Figure 2). a) Share to be considered according to “Miner extended” wit

29、h ni NDDIN 743-4:2012-10 8 b) Share to be considered with ni NDKey 1 Share not taken into account Figure 2 Method according to Miner extended NOTE The cumulative damage theory according to Palmgren-Miner, here abbreviated to “Miner”, is the basis of most of the methods applied for service life calcu

30、lation considering the effect of cyclic, changing loads in a component. “Miner extended” also takes into account shares of stress below fatigue strength which can contribute to total damage due to crack formation.Experience has shown that this method approximates results of exact analyses adequately

31、 for practical calculations. 4.2.2.3 Equivalent damaging stress amplitude The equivalent damaging stress amplitude is to be calculated using Equation (6). zd,ba= zd,ba1/KKor tta= tta1/KKt(6) where zd,ba1or ta1is the amplitude of that share of the spectrum representing the highest load. Here, zd,ba1o

32、r ta1is a reference quantity that can be replaced by any nominal stress amplitude. The load spectrum factor KK,tis to be determined using Equation (7). The load spectrum factor becomes: tttt,111M,KqqDvK +=(7) DMallows for deviations from the limit of the Miner sum. Statistical investigations have sh

33、own that DMcan be significantly smaller than 1. According to 1, 4 DM = 0,3 (8) is recommended. DIN 743-4:2012-10 9 Based on own experience, DM 0,3 can be chosen (in general: 0,3 DM 1). Other determinations shall be specified in the documentation (ND, DM, q,t). The shape of the load spectrum v, t, ta

34、king into account the composition of the load spectrum and determining the equivalent damaging stress amplitude by Equation (6) or (7), is: 1 1bazd,baizd,i*qkiqNn=n (9) ttttntqkiqNn=1 1aaii*(10) a) Fatigue strength domain: Sum limit k (see Figure 2a). It is assumed that only those load bins of the l

35、oad spectrum contribute to damage, whose sum of load cycle numbers is equal to or smaller than the load cycle number NDof the salient point of the Whler curve. Load bins of the load spectrum, whose sum of load cycles exceeds ND, are cut off at ND. For the last bin, i = k, to be considered, set ni =

36、k= neand reduce the total number of bins of the load spectrum j to the number of bins of the load spectrum k. Load bin k is the first one to exceed the salient point of the Whler curve or just to reach it (see fatigue strength, Fig. 2 a) or the last one, with the total sum ni, before the salient poi

37、nt NDof the Whler curve (see limited life strength, Fig. 2 b). b) Limited life strength domain: The sum limit k is equal to the total number j of load spectrum bins k = j If the total number of load cycles is in the fatigue strength domain, then: =11i1DeDi;kijinNnNn (11) If the total number of load

38、cycles is in the limited life strength domain, then: )(,;j1eDijknnNnji=(12) The following applies with respect to the reference number of load cycles N*: N* = ND, if =jiNn1Di(13) =jinN1i* , if =jiNn1Di(14) DIN 743-4:2012-10 10 where j is the total number of load spectrum bins; k is the number of tha

39、t bin of the load spectrum meeting the two conditions =kiNn1Diand =11DikiNn niis the total number of load cycles occurring in a bin. 4.3 Combined loads In the case of combined loads, e.g. bending (and/or tension/compression) and torsion, the relevant safety factor is to be calculated using Equation

40、(15). The calculation shall be based on zd,bADKor tADKas a function of mvor tmvaccording to DIN 743-1 or the resulting values zd,bANK, tANK(Equation (2)*). The equivalent damaging stress amplitudes zd,baor ta(Equation (6) are determined on the basis of the specified theory. Limited life strength: 22

41、1zda ba tazdANK bANK tANKS= + (15) Fatigue strength: 221zda ba tazdADK bADK tADKS= + (16) The load cases mv= constant (tmv= constant) or a/mv= constant(ta/mv= constant) shall be used as a basis. Thus, these quantities are equal for all load bins and remain constant when the load is increased. *)Tran

42、slators note. Should read “Equations (2) and (3)”. DIN 743-4:2012-10 11 Bibliography 1 FKM-Richtlinie: Rechnerischer Festigkeitsnachweis fr Maschinenbauteile. Forschungskuratorium Maschinenbau (FKM), VDMA-Verlag Frankfurt/Main 2003 2 Haibach E.: Betriebsfestigkeit, VDI Verlag 1989 3 Linke H.: Stirnr

43、adverzahnungen Hanser Verlag 1996 4 Eulitz, K.G.: Beurteilung der Zuverlssigkeit von Lebensdauervorhersagen nach dem Nennspannungs-konzept und dem rtlichen Konzept anhand einer Sammlung von Betriebsfestigkeitsversuchen. Habili-tationsschrift, TU Dresden 1999 5 FVA-Richtlinie R 743: Erfassung von Lastkollektiven und Berechnung der Sicherheit im Dauer- und Zeitfestigkeitsbereich 6 Gudehus, H., Zenner, H.: Leitfaden fr eine Betriebsfestigkeitsrechnung, Verlag Stahleisen mbH Dsseldorf 1995