1、BRITISH STANDARDBS ISO 6336-3:2006Incorporating corrigendum June 2008Calculation of load capacity of spur and helical gears Part 3: Calculation of tooth bending strengthICS 21.200 g49g50g3g38g50g51g60g44g49g42g3g58g44g55g43g50g56g55g3g37g54g44g3g51g40g53g48g44g54g54g44g50g49g3g40g59g38g40g51g55g3g36
2、g54g3g51g40g53g48g44g55g55g40g39g3g37g60g3g38g50g51g60g53g44g42g43g55g3g47g36g58BS ISO 6336-3:2006This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 October 2006 BSI 2008ISBN 978 0 580 63410 9National forewordThis British Standard is the UK i
3、mplementation of ISO 6336-3:2006, incorporating corrigendum June 2008. It supersedes BS ISO 6336-3:1996 which is withdrawn.The start and finish of text introduced or altered by corrigendum is indicated in the text by tags. Text altered by ISO corrigendum June 2008 is indicated in the text by .The UK
4、 participation in its preparation was entrusted to Technical Committee MCE/5, Gears.A list of organizations represented on this committee can be obtained on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its
5、 correct application.Compliance with a British Standard cannot confer immunity from legal obligations. Amendments/corrigenda issued since publicationDate Comments30 September 2008 Implementation of ISO corrigendum June 2008Reference numberISO 6336-3:2006(E)INTERNATIONAL STANDARD ISO6336-3Second edit
6、ion2006-09-01Calculation of load capacity of spur and helical gears Part 3: Calculation of tooth bending strength Calcul de la capacit de charge des engrenages cylindriques dentures droite et hlicodale Partie 3: Calcul de la rsistance la flexion en pied de dent BS ISO 6336-3:2006ii iiiContents Page
7、Foreword. v Introduction . vi 1 Scope . 1 2 Normative references . 1 3 Terms, definitions, symbols and abbreviated terms. 1 4 Tooth breakage and safety factors . 2 5 Basic formulae 2 5.1 Safety factor for bending strength (safety against tooth breakage), SF2 5.2 Tooth root stress, F2 5.3 Permissible
8、 bending stress, FP. 4 6 Form factor, YF8 6.1 General. 8 6.2 Calculation of the form factor, YF: Method B . 9 6.3 Derivations of determinant normal tooth load for spur gears . 13 7 Stress correction factor, YS. 14 7.1 Basic uses . 14 7.2 Stress correction factor, YS: Method B. 14 7.3 Stress correcti
9、on factor for gears with notches in fillets. 15 7.4 Stress correction factor, YST, relevant to the dimensions of the standard reference test gears. 15 8 Helix angle factor, Y15 8.1 Graphical value . 16 8.2 Determination by calculation. 16 9 Rim thickness factor, YB. 16 9.1 Graphical values . 16 9.2
10、Determination by calculation. 17 10 Deep tooth factor, YDT18 10.1 Graphical values . 18 10.2 Determination by calculation. 18 11 Reference stress for bending 19 11.1 Reference stress for Method A 19 11.2 Reference stress, with values F limand FEfor Method B 19 12 Life factor, YNT. 19 12.1 Life facto
11、r, YNT: Method A 19 12.2 Life factor, YNT: Method B 19 13 Sensitivity factor, YT, and relative notch sensitivity factor, Y rel T. 21 13.1 Basic uses . 21 13.2 Determination of the sensitivity factors . 21 13.3 Relative notch sensitivity factor, Y rel T: Method B. 22 14 Surface factors, YR, YRT, and
12、relative surface factor, YR rel T27 14.1 Influence of surface condition. 27 BS ISO 6336-3:2006iv 14.2 Determination of surface factors and relative surface factors. 28 14.3 Relative surface factor, YR rel T: Method B 28 15 Size factor, YX30 15.1 Size factor, YX: Method A . 30 15.2 Size factor, YX: M
13、ethod B . 30 Annex A (normative) Permissible bending stress, FP, obtained from notched, flat or plain polished test pieces 33 Annex B (informative) Guide values for mean stress influence factor, YM. 40 Bibliography . 42 BS ISO 6336-3:2006vForeword ISO (the International Organization for Standardizat
14、ion) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a subject for which a technical committee has been established has the right to be r
15、epresented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards
16、 are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an Internat
17、ional Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 6336-3 was
18、 prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity calculation. This second edition cancels and replaces the first edition (ISO 6336-3:1996), Clauses 5 and Clause 9 of which have been technically revised, with a new Clause 8 having been added to this new edition. It
19、also incorporates the Technical Corrigendum ISO 6336-3:1996/Cor.1:1999. ISO 6336 consists of the following parts, under the general title Calculation of load capacity of spur and helical gears: Part 1: Basic principles, introduction and general influence factors Part 2: Calculation of surface durabi
20、lity (pitting) Part 3: Calculation of tooth bending strength Part 5: Strength and quality of materials Part 6: Calculation of service life under variable load BS ISO 6336-3:2006vi Introduction The maximum tensile stress at the tooth root (in the direction of the tooth height), which may not exceed t
21、he permissible bending stress for the material, is the basis for rating the bending strength of gear teeth. The stress occurs in the “tension fillets” of the working tooth flanks. If load-induced cracks are formed, the first of these often appears in the fillets where the compressive stress is gener
22、ated, i.e. in the “compression fillets”, which are those of the non-working flanks. When the tooth loading is unidirectional and the teeth are of conventional shape, these cracks seldom propagate to failure. Crack propagation ending in failure is most likely to stem from cracks initiated in tension
23、fillets. The endurable tooth loading of teeth subjected to a reversal of loading during each revolution, such as “idler gears”, is less than the endurable unidirectional loading. The full range of stress in such circumstances is more than twice the tensile stress occurring in the root fillets of the
24、 loaded flanks. This is taken into consideration when determing permissible stresses (see ISO 6336-5). When gear rims are thin and tooth spaces adjacent to the root surface narrow (conditions which can particularly apply to some internal gears), initial cracks commonly occur in the compression fille
25、t. Since, in such circumstances, gear rims themselves can suffer fatigue breakage, special studies are necessary. See Clause 1. Several methods for calculating the critical tooth root stress and evaluating some of the relevant factors have been approved. See ISO 6336-1. BS ISO 6336-3:20061Calculatio
26、n of load capacity of spur and helical gears Part 3: Calculation of tooth bending strength IMPORTANT The user of this part of ISO 6336 is cautioned that when the method specified is used for large helix angles and large pressure angles, the calculated results should be confirmed by experience as by
27、Method A. 1 Scope This part of ISO 6336 specifies the fundamental formulae for use in tooth bending stress calculations for involute external or internal spur and helical gears with a rim thickness sR 0,5 htfor external gears and sR 1,75 mnfor internal gears. In service, internal gears can experienc
28、e failure modes other than tooth bending fatigue, i.e. fractures starting at the root diameter and progressing radially outward. This part of ISO 6336 does not provide adequate safety against failure modes other than tooth bending fatigue. All load influences on tooth stress are included in so far a
29、s they are the result of loads transmitted by the gears and in so far as they can be evaluated quantitatively. The given formulae are valid for spur and helical gears with tooth profiles in accordance with the basic rack standardized in ISO 53. They may also be used for teeth conjugate to other basi
30、c racks if the virtual contact ratio nis less than 2,5. The load capacity determined on the basis of permissible bending stress is termed “tooth bending strength”. The results are in good agreement with other methods for the range, as indicated in the scope of ISO 6336-1. 2 Normative references The
31、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 amendments) applies. ISO 53:1998, Cylindrical gears for general and heavy
32、engineering Standard basic rack tooth profile ISO 1122-1:1998, Vocabulary of gear terms Part 1: Definitions related to geometry ISO 6336-1:2006, Calculation of load capacity of spur and helical gears Part 1: Basic principles, introduction and general influence factors ISO 6336-5:2003, Calculation of
33、 load capacity of spur and helical gears Part 5: Strength and quality of material 3 Terms, definitions, symbols and abbreviated terms For the purposes of this document, the terms, definitions, symbols and abbreviated terms given in ISO 1122-1 and ISO 6336-1 apply. BS ISO 6336-3:20062 4 Tooth breakag
34、e and safety factors Tooth breakage usually ends the service live of a transmission. Sometimes, the destruction of all gears in a transmission can be a consequence of the breakage of one tooth. In some instances, the transmission path beween input and output shafts is broken. As a consequence, the c
35、hosen value of the safety factor SFagainst tooth breakage should be larger than the safety factor against pitting. General comments on the choice of the minimum safety factor can be found in ISO 6336-1:2006, 4.1.7. It is recommended that manufacturer and customer agree on the value of the minimum sa
36、fety factor. This part of ISO 6336 does not apply at stress levels above those permissible for 103cycles, since stresses in this range may exceed the elastic limit of the gear tooth. 5 Basic formulae The actual tooth root stress Fand the permissible (tooth root) bending stress FPshall be calculated
37、separately for pinion and wheel; Fshall be less than FP. 5.1 Safety factor for bending strength (safety against tooth breakage), SFCalculate SFseparately for pinion and wheel: FG1F1 FminF1SS= W (1) FG2F2 FminF2SS= W (2) F1and F2are derived from Equations (3) and (4). The values of FGfor reference st
38、ress and static stress are calculated in accordance with 5.3.2.1 and 5.3.2.2, using Equation (5). For limited life, FGis determined in accordance with 5.3.3. The values of tooth root stress limit FG, of permissible stress FPand of tooth root stress Fmay each be determined by different methods. The m
39、ethod used for each value shall be stated in the calculation report. NOTE Safety factors in accordance with the present clause are relevant to transmissible torque. See ISO 6336-1:2006, 4.1.7 for comments on numerical values for the minimum safety factor and risk of damage. 5.2 Tooth root stress, FT
40、ooth root stress Fis the maximum tensile stress at the surface in the root. 5.2.1 Method A In principle, the maximum tensile stress can be determined by any appropriate method (finite element analysis, integral equations, conformal mapping procedures or experimentally by strain measurement, etc.). I
41、n order to determine the maximum tooth root stress, the effects of load distribution over two or more engaging teeth and changes of stress with changes of meshing phase shall be taken into consideration. Method A is only used in special cases and, because of the great effort involved, is only justif
42、iable in such cases. BS ISO 6336-3:200635.2.2 Method B According to this part of ISO 6336, the local tooth root stress is determined as the product of nominal tooth root stress and a stress correction factor 1). This method involves the assumption that the determinant tooth root stress occurs with a
43、pplication of load at the outer point of single pair tooth contact of spur gears or of the virtual spur gears of helical gears. However, in the latter case, the “transverse load” shall be replaced by the “normal load”, applied over the facewidth of the actual gear of interest. For gears having virtu
44、al contact ratios in the range 2 u n2, it is necessary to substitute the relevant total tangential load as Ft. Reasons for the choice of load application at the reference cylinder are given in 6.3. See ISO 6336-1, 4.2, for definition of Ftand comments on particular characteristics of double helical
45、gears. 3) The value b, of mating gears, is the facewidth at the root circle, ignoring any intentional transverse chamfers or tooth-end rounding. If the facewidths of the pinion and wheel are not equal, it can be assumed that the load bearing width of the wider facewidth is equal to the smaller facew
46、idth plus such extension of the wider that does not exceed 1 the module at each end of the teeth. BS ISO 6336-3:200655.3.1.1 Method A By this method, the values for FPor for the tooth root stress limit, FG, are obtained using Equations (3) and (4) from the S-N curve or damage curve derived from resu
47、lts of testing facsimiles of the actual gear pair, under the appropriate service conditions. The cost required for this method is, in general, only justifiable for the development of new products, failure of which would have serious consequences (e.g. for manned space flights). Similarly, in line wi
48、th this method, the allowable stress values may be derived from consideration of dimensions, service conditions and performance of carefully monitored reference gears. 5.3.1.2 Method B Damage curves characterized by the nominal stress number (bending), F lim, and the factor YNThave been determined f
49、or a number of common gear materials and heat treatments from results of gear load or pulsator testing of standard reference test gears. Material values so determined are converted to suit the dimensions of the gears of interest, using the relative influence factors for notch sensitivity, Y rel T, for surface roughness, YR rel T, and for size, YX. Method B is recommended for the calculation of reasonably accurate gear ratings whenever bending strength values are available from gear tests, from special tests or, if the ma
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