1、December 2012 Translation by DIN-Sprachendienst.English price group 13No 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+“2096508www.din.deDDIN 743-1Calculation of load capacity of shafts and axles Part 1: General,English translation of DIN 743-1:2012-12Tragfhigkeitsberechnung von Wellen und Achsen Teil 1: Grundlagen,Englische bersetzung von DIN 743-1:2012-12Calcul de la capacit des abres et axes Part
3、ie 1: Base,Traduction anglaise de DIN 743-1:2012-12SupersedesDIN 743-1:2000-10www.beuth.deDocument comprises 25 pagesIn case of doubt, the German-language original shall be considered authoritative.08.15 DIN 743-1:2012-12 2 A comma is used as the decimal marker. Contents Page Foreword 3 Introduction
4、 .5 1 Scope 6 2 Normative references 7 3 Symbols, designations and units .7 4 Proof of avoidance of fatigue failure .9 4.1 Factor of safety 9 4.2 Working stresses 10 4.3 Fatigue strength value . 10 5 Proof of avoidance of permanent deformation, incipient cracking or overload breakage under maximum l
5、oad 14 5.1 Safety factor 14 5.1.1 Proof of avoidance of permanent deformation 15 5.1.2 Proof of avoidance of incipient cracking (and/or overload breakage) in hard surfaces . 16 5.2 Component yield point . 16 5.3 Components incipient crack limit 17 5.4 Working stresses (maximum stresses) 18 Annex A (
6、informative) Explanations of the variation of load and/or stress, cross-sectional areas and the reading of ADKfrom the Smith diagram . 19 Annex B (normative) Schema of the safety factor calculation 22 B.1 General schema 22 B.2 Total influence factor . 24 Bibliography . 25 Figures Figure A.1 Variatio
7、n of applied load with time (Fzd,Mb,Mt) and stress (zd,b,tt) 19 Figure A.2 Origination of amplitude of bending moment Mbas a result of shaft rotation (rotational bending); force F with constant direction, shaft rotating ( )02 = n . 19 Figure A.3 Cross section parameters . 19 Figure A.4 Load cases, r
8、epresented in the fatigue strength diagram (Smith diagram) . 20 Figure A.5 Fatigue strength diagram with extension of the compression zone (component pressure yield point dFK) 21 Figure B.1 Calculation procedure for safety factors . 23 Figure B.2 Calculation procedure for total influence factor K,t2
9、4 DIN 743-1:2012-12 3 Tables Table 1 Determination of working stresses 10 Table 2 Increase factor for yield point Fat circumferential notch (and/or according to DIN 743-2) and materials without hard surface. 17 Table 3 Static support factor K2Ffor materials without hard surface 17 Table 4 Determinat
10、ion of maximum stresses (maximum nominal stresses) 18 Table A1 ADKin the marked compression zone for load case 1 with mvIf this condition is not fulfilled, Table A.1 and Figure A.5 (Annex A) shall be used. The influence factors for mean stress sensitivity shall be calculated using Equations (20) to
11、(22): ( ) ( )zdWKBBeff1zdWKKzd2 =ddK(20) ( ) ( )bWKBBeff1bWKKb2 =ddK(21) ( ) ( )tWKBBeff1tWKK2 ttt=ddK(22) where K1(deff) is the technological size influence factor (heat treating quality, hardenability) according to DIN 743-2 for tensile strength; B is the tensile strength for test bar diameter dB.
12、 The combined mean stresses (von Mises) shall be calculated using Equations (23) and (24): ( )2tm2bmzdmmv3 t += (23) 3mvmvt = (24) 5 Proof of avoidance of permanent deformation, incipient cracking or overload breakage under maximum load 5.1 Safety factor The calculated safety factor S shall be equal
13、 to or greater than the minimum safety factor Smin(S Smin; see explanations of Equation (1). The principles of the calculation method require a minimum safety factor Smin= 1,2. Uncertainties in the estimation of the maximum load, possible consequential damage, etc. require higher safety factors. The
14、se shall be agreed upon or otherwise determined. On principle, it shall be established that permanent deformation and incipient cracks are avoided. If there is no risk of brittle fracture (B 1 300 N/mm2), incipient cracks and overload breakage do not generally occur on structural and quenched and te
15、mpered steels at maximum load within the usual area of application prior to permanent component deformation. In this case it is sufficient to prove that permanent deformation of the macro geometry is avoided. DIN 743-1:2012-12 15 Also on shafts with a hard surface (e.g. case hardened shafts), perman
16、ent component deformation can occur prior to an incipient cracking (mainly dependent on the stress concentration at the notch and the core hardness). Since the hardened case is not ductile it shall be proved that permanent deformation below the case and incipient cracking and/or overload breakage in
17、 the case are avoided. If max 0,2 B, it shall be checked on tempering steels and high-tensile steels with B 1 300 N/mm2whether the ductility is sufficient to reduce the stress peak by plastic deformation. An incipient crack does not yet occur with max 0,2and a stress concentration factor of 10 and a
18、t least 4 % local plastic ductility of the material. The local plastic ductility is greater than the elongation on fracture. This can serve as a rough guide if no specially determined values are available. For max 0,2 ,stress calculations shall be made following highly sophisticated analysis methods
19、 (e.g. FEM, BEM) or by carrying out experimental tests to check the risk of incipient cracking. 5.1.1 Proof of avoidance of permanent deformation Proof of avoidance of permanent deformation shall be furnished. It does not refer to the avoidance of local deformations (e.g. in the notch root), but to
20、the avoidance of permanent deformations in larger areas of the component (unacceptable dimensional deviations, deviations exceeding the tolerance value). In the case of hard surfaces, the avoidance of permanent deformations below the hard surface shall be examined. For such areas it is assumed that
21、the notch effect has faded. The calculated factor of safety against permanent deformation resulting from combined stresses (composed of tension/compression, bending, and torsion) shall be calculated with Equation (25) taking into account the scope of validity mentioned in 5.1. Compressive stresses s
22、hall be used in Equation (25) with a negative sign. 2tFKtmax2bFKbmaxzdFKzdmax1+=S(25) If only bending or torsion is present, then for bending: bmaxbFK=S (26) for torsion: tmaxtFKtt=S (27) (Equation (26) is likewise valid for tension/compression by replacing bmaxwith zdmaxand bFKwith zdFK.) In the ab
23、ove zdFK, bFK, ttFKare the component yield points for tension/compression, bending and/or torsion (see 5.2) zdmax, bmax, ttmax are the existing maximum nominal stresses as a result of the operating load. They are determined by means of Table 5, using the maximum occurring loads Fzdmax, Mbmax and Mtm
24、ax. NOTE In the case of materials for highly stressed shafts with hard surfaces it is recommended to consider the actual hardness and/or strength progression into the core of the material and compare it with the slope of stress. If no knowledge is available here, calculations to prove the avoidance
25、of plastic deformation below the surface can be made by approximation with the maximum nominal stress on the surface, and this maximum nominal stress can then be compared with the yield strength of the core. DIN 743-1:2012-12 16 5.1.2 Proof of avoidance of incipient cracking (and/or overload breakag
26、e) in hard surfaces The calculated factor of safety against incipient cracking and/or overload breakage as a result of combined stresses composed of tension/compression, bending, and torsion shall be calculated using Equation (28) (direct stress theory): + +=2tBRandtmax2bBRandbmaxbzdBRandzdmaxzdbBRa
27、ndbmaxbzdBRandzdmaxzd25,01tttS (28) Here, the local stresses are decisive. If bending or torsion only is present, then for bending: bbmaxRandbB S= (29) for torsion: ttt S=tmaxRandtB(30) (Equation (29) is likewise valid for tension/compression by replacing bmaxwith zdmaxand bB RandwithzdB Rand.) wher
28、e zd,b, tare the stress concentration factors for tension/compression, bending and/or torsion zdBRand, bBRand, ttBRand are the breaking points in the hard surface in the case of tension/compression, bending and/or torsion (see 5.3) If the stress concentration factors or local stresses are not known,
29、 the fatigue notch factors can be used by approximation. 5.2 Component yield point The component yield point is taken as the basis of the calculation of the factor of safety against permanent deformation. The starting point is the yield strength S(d) at the cross section of the component in question
30、. If this is not known, S(d) can be determined by approximation from the yield strength valid for the test bar diameter dB(reference diameter) and a size factor K1(deff) (i.e. S(d) = S(dB)K1(deff). When applying this method, the component yield point shall be calculated using Equation (31) and/or (3
31、2). )()(BSFF2eff1bFKzd,dKdK = (31) 3/)()(BSFF2eff1tFKdKdK t = (32) DIN 743-1:2012-12 17 In the above K1(deff) is the technological size influence factor (heat treating quality, hardenability) according to DIN 743-2 for the yield strength; K2Fis the static support factor according to Table 3 as a res
32、ult of local plastic deformation on the surface. On hard surfaces, K2F= 1 (for the calculation to be made for the value below the surface); F is the factor increasing the yield point as a result of the multi-axial stress condition at the circumferential notch and local hardness increase according to
33、 Table 2. In the case of hard surfaces or no circumferential notch, F= 1; S(dB) is the yield strength for the reference diameter dBaccording to DIN 743-3; in the case of hard surfaces, the values for the core apply. Table 2 Increase factor for yield point Fat circumferential notch (and/or according
34、to DIN 743-2) and materials without hard surface Type of stress or FTension/compression or bending up to 1,5 1,00 1,5 to 2,0 1,05 2,0 to 3,0 1,10 above 3,0 1,15 Torsion Any 1 NOTE As a result of the multi-axial stress condition (e.g. also at circumferential notches), the yield point of the component
35、 is increased by F, but the risk of low-ductility fractures increases. Table 3 Static support factor K2Ffor materials without hard surface Type of stress K2FSolid shaft Hollow shaft Tension/compression 1,0 1,0 Bending 1,2 1,1 Torsion 1,2 1,0 5.3 Components incipient crack limit Proof is required for
36、 hard surfaces and tempering steels with B 1 300 N/mm2, if the local ductility is below 4 %. The incipient crack limits of the component shall be calculated on the basis of the resistances to breaking of the hard surfaces using Equation (33) and/or (34) (for brittle materials). zd,bBRand= BRand (33)
37、 ttBRand= BRand (34) DIN 743-1:2012-12 18 The starting point is the surface hardness on the real component. With a hardness of 700.800 HV (e.g. case hardness) calculations can use a tensile strength in the surface of BRand= 2 300 N/mm2, neglecting the residual stresses. If the surface has been treat
38、ed or hardened in another way, the tensile strength in the surface can be approximately determined according to DIN EN ISO 18265:2004 (Table A.1). Tempering steels with nitrided or nitrocarburized surfaces do have tensile strengths of BRand 1 700 N/mm2in the surface. NOTE BRandis increased by the co
39、mpressive residual stresses which generally exist in the hard surface. 5.4 Working stresses (maximum stresses) The working stresses are to be calculated according to Table 4. Table 4 Determination of maximum stresses (maximum nominal stresses) Type of stress Working stress3)Cross-sectional area and/
40、or section modulus Tension/compression AFzdmaxzdmax= )(42i2ddA= Bending bbmaxbmaxWM= dddW)(32=4i4bTorsion ttmaxtmax=WMt dddWt)(164i4= 3) See Figure A.1. DIN 743-1:2012-12 19 Annex A (informative) Explanations of the variation of load and/or stress, cross-sectional areas and the reading of ADKfrom th
41、e Smith diagram t = time Figure A.1 Variation of applied load with time (Fzd,Mb,Mt) and stress (zd,b,tt) Figure A.2 Origination of amplitude of bending moment Mbas a result of shaft rotation (rotational bending); force F with constant direction, shaft rotating ( )02 = n Figure A.3 Cross section para
42、meters DIN 743-1:2012-12 20 Key F1 = Load case 1 F2 = Load case 2 NOTE The marked area in the Smith diagram is defined by the intersection point of the line UDKextended into the compression zone with the line, given by the pressure yield point dFK,parallel to the abscissa. The boundary lines in the
43、fatigue strength diagram (Smith diagram) ODKand UDKrepresent an approximation to the actual behaviour. Figure A.4 Load cases, represented in the fatigue strength diagram (Smith diagram) DIN 743-1:2012-12 21 Key F1 = Load case 1 F2 = Load case 2 NOTE The marked area in the Smith diagram is defined by
44、 the intersection point of the line UDKextended into the compression zone with the line, given by the pressure yield point dFK,parallel to the abscissa. Figure A.5 Fatigue strength diagram with extension of the compression zone (component pressure yield point dFK) Table A1 ADKin the marked compressi
45、on zone for load case 1 with mv0 DIN 743-1:2012-12 22 Annex B (normative) Schema of the safety factor calculation B.1 General schema Figure B.1 (continued) Calculation of fatigue safety factor Calculation of yield point safety factor Stresses (ampli-tudes) zda,ba,ttaMaterial fatigue limits under rev
46、ersed stress zdW(dB), bW(dB), ttW(dB) Minimum safety factor SminStresses (maximum values) zdmax,bmax,ttmaxYield strength, tensile strength S(dB), B(dB) Minimum safety factor SminComponent fatigue limits under reversed stress zdWK= f(K1,K,zdW) bWK= f(K1,K,bW) ttWK= f(K1,Kt,ttW) Stress amplitude of co
47、mponent fatigue strength zdADK= f(zdWK,mv) bADK= f(bWK,mv) ttADK= f(ttWK,tmv) Component yield points zd,bFK= K1(d)K2FFS(dB) ttFK= K1(d)K2FFS(dB)/3 Incipient crack limit of component: See DIN 743-1, 5.1.2 Safety factor against fatigue failure: 2tADKta2bADKbazdADKzda1+=ttSSafety factor against yielding: 2tFKtmax2bFKbmaxzdFKzdmax1+=ttSSafety factor against incipient cracking: See DIN 743-1, 5.1.2 S Smin; (Sminagreed) S Smin; (Sminagreed) DIN 743-1:2012-12 23 Key WK,WKComponent fatigue limits under reversed st
