DIN 743 Bb 1-2012 Calculation of load capacity of shafts and axles - Supplement 1 Examples to part 1 to 3《轴和柄负载能力的计算 补充件1 第1至3部分的实例》.pdf

1、December 2012 Translation by DIN-Sprachendienst.English price group 11No 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!%?CQ“2283246www.din.deDThis supplement provides information relating to DIN 743, but does not contain any additional specifications.DIN 743 Supplement 1Calculation of load capacity of shafts and axles Supplement 1: Examples to part 1 to 3,English translation of DIN 743 Beiblatt 1:2012-1

3、2Tragfhigkeitsberechnung von Wellen und Achsen Beiblatt 1: Anwendungsbeispiele zu Teil 1 bis 3,Englische bersetzung von DIN 743 Beiblatt 1:2012-12Calcul de la capacit des arbres et axes Supplment 1: Exemples avec partie 1 3,Traduction anglaise de DIN 743 Beiblatt 1:2012-12SupersedesDIN 743 Supplemen

4、t 1:2000-10www.beuth.deDocument comprises 20 pagesIn case of doubt, the German-language original shall be considered authoritative.09.15 DIN 743 Supplement 1:2012-12 2 A comma is used as the decimal marker. Contents Page Foreword 3 1 Normative references 4 2 Symbols, designations and units .4 3 Appl

5、ication examples 6 3.1 Calculation of the factor of safety against fatigue failure and permanent deformation for a shouldered shaft in bending and torsion according to Figure 1 6 3.2 Calculation of the factor of safety against fatigue failure and permanent deformation for a parallel key connection i

6、n rotational bending and constant torsion according to Figure 2. 12 3.3 Calculation of the factor of safety against fatigue failure and permanent deformation for an axle with groove for circlip in bending according to Figure 3 16 DIN 743 Supplement 1:2012-12 3 Foreword This supplement has been prepa

7、red by Working Committee NA 060-34-32 AA Wellen- und Well-Nabe-Verbindungen of Section Antriebstechnik of the Normenausschuss Maschinenbau (Mechanical Engineering Standards Committee) in DIN. DIN 743 Calculation of load capacity of shafts and axles comprises: Part 1: General Part 2: Theoretical stre

8、ss concentration factors and fatigue 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 document differs from DIN 743 Supplement 1:2000-10 as

9、 follows: a) Subclause 4.3 “Calculation of the factor of safety against fatigue failure and permanent deformation for an axle with shoulder and undercut in bending (example)” has been replaced by Subclause 3.3 “Calculation of the factor of safety against fatigue failure and permanent deformation for

10、 an axle with groove for circlip in bending according to Figure 3”; b) the document has been editorially revised. DIN 743 Supplement 1:2012-12 4 1 Normative references DIN 743-1, Calculation of load capacity of shafts and axles Part 1: General DIN 743-2, Calculation of load capacity of shafts and ax

11、les Part 2: Theoretical stress concentration factors and fatigue notch factors DIN 743-3, Calculation of load capacity of shafts and axles Part 3: Strength of materials 2 Symbols, designations and units Symbol Designation Unit d Component diameter at notch cross section; in ring cross section: wall

12、thickness mm dBMaterial reference diameter mm dBKNotch reference diameter mm deffDiameter relevant for heat treatment mm n Sensitivity factor r Notch radius mm G Relative stress gradient mm-1RzAverage peak-to-valley height m S Calculated factor of safety K,Total influence factor K1(deff) Technologic

13、al size influence factor K2(d) Geometrical size influence factor (for the unnotched, polished round bar) K3(d) Geometrical size influence factor (for the fatigue notch factor) K2FStatic support factor KF, KFInfluence factor for surface roughness KvInfluence factor for surface conditioning , Stress c

14、oncentration factor , Fatigue notch factor FIncrease factor for yield point zd,bW, tWMaterial fatigue limit under reversed stress for reference diameter dB N/mm zd, bWK, tWKComponent fatigue limit under reversed stress N/mm zd,bADK, tADKStress amplitude of component fatigue strength for defined mean

15、 stress N/mm zd,bODK, tODKMaximum stress for component fatigue strength for defined mean stress N/mm DIN 743 Supplement 1:2012-12 5 Symbol Designation Unit m, mMean stress1)N/mm a, taStress amplitude1)N/mm o, oMaximum stress1)N/mm u, uMinimum stress1) N/mm zd,bFK, tFKComponent yield point N/mm B, (R

16、m) Tensile strength N/mm S, (Re,Rp0,2) Yield strength N/mm bFBending yield point N/mm tFTorsion yield point N/mm K, KInfluence factor for mean stress sensitivity Subscripts a Existing amplitude b Bending bW Reversed bending t, Torsion tW Reversed torsion Bending v von Mises stress (combined effectiv

17、e stresses) A Endurable amplitude D Fatigue strength K Notched component W Alternating 1)Nominal stress DIN 743 Supplement 1:2012-12 6 3 Application examples 3.1 Calculation of the factor of safety against fatigue failure and permanent deformation for a shouldered shaft in bending and torsion accord

18、ing to Figure 1 This example solely serves to demonstrate the procedure of calculation. In general, this load case is not usual for a shaft. Figure 1 Shouldered shaft Given: Dimensions: D = 50 mm d = 42 mm r = 5 mm t = 4 mm Load (cross section at d) b = bm ba = 500 N/mm 50 N/mm t= tm ta= 100 N/mm 30

19、 N/mm Material: 34CrMo4 (ultimate strength values according to DIN 743-3, dB 16 mm) Average peak-to-valley height: Rz= 5 m Required: Calculated factor of safety to prove the fatigue strength for load case 1 and calculated factor of safety against exceeding the yield point. Calculation: For the schem

20、a, see Annex B to DIN 743-1. The calculation is to be made with fatigue notch factors for notches with a known stress concentration factor according to DIN 743-2. DIN 743 Supplement 1:2012-12 7 a) Total influence factor for bending Stress concentration factor according to Figure 9 in DIN 743-2 with

21、d/D = 0,84; r/t = 1,25; r/d = 0,119 = 1,557 Relative stress gradient G according to Table 2 in DIN 743-2 with = 0,179 G = 0,542 mm-1 Technological size influence factor K1(deff)2)according to Equations (12) and (14) or Figure 13 in DIN 743-2 with dB= 16 mm and deff= 50 mm. Tensile strength: Yield st

22、rength: Sensitivity factor n according to Equation (5) or Figure 4 in DIN 743-2 with S(d) = K1(deff) S(dB) = 665,6 N/mm2 Fatigue notch factor according to Equation (4) in DIN 743-2 =/n = 1,557/1,04 = 1,497 Geometrical size influence factor K2(d) according to Equation (16) or Figure 14 in DIN 743-2 2

23、)K1(deff) is determined for diameter D. This is to take into account that the shaft in pre-machined condition (with small machining allowance) will be quenched and tempered. During this heat treatment (quenching or hardening) diameter D influences the endangered section with diameter d at the transi

24、tion radius. DIN 743 Supplement 1:2012-12 8 Influence factor for surface roughness KFaccording to Equation (18) or Figure 16 in DIN 743-2 with B(d), 21/871)()()( mmNdKddeffBBB= Influence factor for surface conditioning KV= 1 Total influence factor Kaccording to Equation (8) in DIN 743-1 b) Total inf

25、luence factor for torsion Stress concentration factor according to Figure 10 in DIN 743-2 with d/D = 0,84; r/t = 1,25; r/d = 0,119 = 1,283 Relative stress gradient G according to Table 2 in DIN 743-2 G = 0,23 mm-1 Technological size influence factor K1(deff)2)according to Equations (12) and (14) or

26、Figure 13 in DIN 743-2 with dB= 16 mm and deff= 50 mm Tensile strength: Yield strength: 2)K1(deff) is determined for diameter D. This is to take into account that the shaft in pre-machined condition (with small machining allowance) will be quenched and tempered. During this heat treatment (quenching

27、 or hardening) diameter D influences the endangered section with diameter d at the transition radius. DIN 743 Supplement 1:2012-12 9 Sensitivity factor n according to Equation (5) or Figure 4 in DIN 743-2 with S(d) = K1(deff) S(dB) = 665,6 N/mm2 Fatigue notch factor according to Equation (4) in DIN

28、743-2 = /n = 1,283/1,026 = 1,250 Geometrical size influence factor K2(d) according to Equation (16) or Figure 14 in DIN 743-2 Influence factor for surface roughness KFaccording to Equation (19) in DIN 743-2 Influence factor for surface conditioning KV= 1 Total influence factor K according to Equatio

29、n (9) in DIN 743-1 c) Calculated factor of safety to prove the fatigue strength according to load case 1 The combined mean stresses (von Mises) according to Equations (23) and (24) in DIN 743-1 DIN 743 Supplement 1:2012-12 10 Component fatigue limit under reversed stress WK, WKaccording to Equations

30、 (6) and (7) in DIN 743-1 Influence factor for mean stress sensitivity ,according to Equations (21) and (22) in DIN 743-1 Stress amplitude of component fatigue strength ADK, tADKaccording to Equations (11) and (12) in DIN 743-1 DIN 743 Supplement 1:2012-12 11 Calculated factor of safety S according

31、to Equation (2) in DIN 743-1 d) Calculated factor of safety S against exceeding the yield point Static support factor K2Ffor bending and torsion according to Table 3 in DIN 743-1 K2F= 1,2; K2F= 1,2 Increase factor for yield point Faccording to Table 2 in DIN 743-1 F= 1,05; F= 1 Component yield point

32、 bFK, tFKaccording to Equations (31) and (32) in DIN 743-1 with K1(deff) = 0,832; Calculated factor of safety S according to Equation (25) in DIN 743-1 The component diameter is determined by the yield point calculation. DIN 743 Supplement 1:2012-12 12 3.2 Calculation of the factor of safety against

33、 fatigue failure and permanent deformation for a parallel key connection in rotational bending and constant torsion according to Figure 2 Figure 2 Straight shaft with parallel keyway Given: Dimensions: d = 50 mm Load: Alternating bending moment: Mb= 1 200 Nm Constant torsional moment: Mt = 3 000 Nm

34、Shock load: Mbmax= 1,5 Mb, Mtmax = 1,5 Mt Material: 42CrMo4 (ultimate strength values according to DIN 743-3; dB 16 mm) B= 1 100 N/mm2; S= 900 N/mm2; zdW= 440 N/mm2; bW= 550 N/mm2; tW= 330 N/mm2Average peak-to-valley height: Rz= 12,5 m Required: Calculated factors of safety to prove the fatigue stre

35、ngth according to load case 1 and to prevent exceeding the yield point. Calculation: For the schema, see Annex B to DIN 743-1. The calculation is made with fatigue notch factors determined by experiment according to DIN 743-2. a) Total influence factor for bending Technological size influence factor

36、 K1(deff) according to Equations (12) and (14) or Figure 13 in DIN 743-2 with dB= 16 mm and deff= 50 mm DIN 743 Supplement 1:2012-12 13 Tensile strength Yield strength Fatigue notch factor valid for reference diameter dBK= 40 mm according to Table 1 in DIN 743-2 with B(d) = (16 mm) BK1(deff= 50 mm)

37、= 958,1 N/mm 2(dBK) = 2,95 Geometrical size influence factor K3(d) and K3(dBK) according to Equation (17) or Figure 15 in DIN 743 -2 Fatigue notch factor valid for component diameter d according to Equation (3) in DIN 743-2 Geometrical size influence factor K2(d) according to Equation (16) or Figure

38、 14 in DIN 743-2 DIN 743 Supplement 1:2012-12 14 Influence factor for surface roughness KFaccording to Table 1 in DIN 743-2 KF= 1 Influence factor for surface conditioning Kv= 1 Total influence factor Kaccording to Equation (8) in DIN 743-1 b) Stress resulting from load and cross section (nominal st

39、ress referred to full cross section) Bending stress amplitude ba Torsional mean stress tmc) Calculated factor of safety to prove the fatigue strength according to load case 1 Combined mean stresses (von Mises) according to Equation (23) in DIN 743-1 Component fatigue limit under reversed stress bWKa

40、ccording to Equation (6) in DIN 743-1 DIN 743 Supplement 1:2012-12 15 Influence factor for mean stress sensitivity bKaccording to Equation (21) in DIN 743-1 Stress amplitude of component fatigue strength bADKaccording to Equation (11) in DIN 743-1 Calculated factor of safety S according to Equation

41、(3) in DIN 743-1 d) Calculated factor of safety S against exceeding the yield point Static support factor K2Ffor bending and torsion according to Table 3 in DIN 743-1 K2F, = 1,2; K2F= 1,2 Increase factor for the yield point Faccording to Table 2 in DIN 743-1 F= 1; F= 1 (no circumferential notch) Com

42、ponent yield point bFK; tFKaccording to Equations (31) and (32) in DIN 743-1 with K1(deff) = 0,832 DIN 743 Supplement 1:2012-12 16 Calculated factor of safety S according to Equation (25) in DIN 743-1 The component diameter is determined by the fatigue strength calculation. 3.3 Calculation of the fa

43、ctor of safety against fatigue failure and permanent deformation for an axle with groove for circlip in bending according to Figure 3 Figure 3 Detail of an axle with groove for circlip Given: Dimensions: D = 80 mm d = 76,5 mm m = 2,65 mm r = 0,25 mm (corresponds to a circlip thickness s = 2,5 mm) DI

44、N 743 Supplement 1:2012-12 17 Load: Mb= Mbm Mba= 8 000 Nm 2 500 Nm Material: E335 (structural steel): An ultimate strength value of B= 590 N/mm2is used for E335 in this example instead of B= 570 N/mm2as given in DIN 743-3 Table A1; dB = 16 mm. B = 590 N/mm2; S= 335 N/mm2; zdW= 235 N/mm2; bW= 290 N/m

45、m2; tW= 180 N/mm2Average peak-to-valley height: Rz= 25 m Required: Calculated factor of safety to prove the fatigue strength for load case 2 and against exceeding the yield point. Calculation: For the schema, see Annex B to DIN 743-1. The calculation is to be made analogously to fatigue notch factor

46、s determined by experiment according to DIN 743-2 (square groove: = f(,nNeuber). a) Total influence factor Technological size influence factor K1(deff)2)according to Equations (10) and (11) in DIN 743-2 with dB= 16 mm and deff= 80 mm Tensile strength: K1(deff) = 1 Yield strength: K1(deff) = 1-0,26lg

47、(deff/2dB) Structural radius * according to Neuber (DIN 743-2, 4.2.4) with S(d) = S(16 mm) K1(deff= 80 mm) = 300,2 N/mm2 Corrected radius rfaccording to DIN 743-2, 4.2.4 with r = 0,25 mm and * = 0,107 mm rf= r + 2,9 * rf= 0,25 mm + 2,9 0,107 mm = 0,56 mm 2)K1(deff) is determined for diameter D. This is to take into account that the shaft in pre-machined condition (with small machining allowance) will be quenched and tempered. During this heat treatment (quenching or hardening) diameter D influences the endangered section