1、BRITISH STANDARD BS ISO 6336-3:2006 Incorporating corrigendum June 2008 Calculation of load capacity of spur and helical gears Part 3: Calculation of tooth bending strength ICS 21.200 BS ISO 6336-3:2006 This British Standard was published under the authority of the Standards Policy and Strategy Comm
2、ittee on 31 October 2006 BSI 2008 ISBN 978 0 580 63410 9 National foreword This British Standard is the UK implementation 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 It supersedes BS ISO 6336-3:1996 which is withdrawn.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
3、 indicated in the text by tags. Text altered by ISO corrigendum June 2008 is indicated in the text by . The UK 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 p
4、ublication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. Compliance with a British Standard cannot confer immunity from legal obligations. Amendments/corrigenda issued since publication Date Comments 30 September 2008 Imple
5、mentation of ISO corrigendum June 2008 Reference number ISO 6336-3:2006(E)INTERNATIONAL STANDARD ISO 6336-3 Second edition 2006-09-01 Calculation of load capacity of spur and helical gears Part 3: Calculation of tooth bending strength Calcul de la capacit de charge des engrenages cylindriques dentur
6、es droite et hlicodale Partie 3: Calcul de la rsistance la flexion en pied de dent BS ISO 6336-3:2006ii iii Contents Page 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 formul
7、ae 2 5.1 Safety factor for bending strength (safety against tooth breakage), S F2 5.2 Tooth root stress, F2 5.3 Permissible bending stress, FP . 4 6 Form factor, Y F8 6.1 General. 8 6.2 Calculation of the form factor, Y F : Method B . 9 6.3 Derivations of determinant normal tooth load for spur gears
8、 . 13 7 Stress correction factor, Y S . 14 7.1 Basic uses . 14 7.2 Stress correction factor, Y S : Method B. 14 7.3 Stress correction factor for gears with notches in fillets. 15 7.4 Stress correction factor, Y ST , relevant to the dimensions of the standard reference test gears. 15 8 Helix angle fa
9、ctor, Y 15 8.1 Graphical value . 16 8.2 Determination by calculation. 16 9 Rim thickness factor, Y B . 16 9.1 Graphical values . 16 9.2 Determination by calculation. 17 10 Deep tooth factor, Y DT18 10.1 Graphical values . 18 10.2 Determination by calculation. 18 11 Reference stress for bending 19 11
10、.1 Reference stress for Method A 19 11.2 Reference stress, with values F limand FEfor Method B 19 12 Life factor, Y NT . 19 12.1 Life factor, Y NT : Method A 19 12.2 Life factor, Y NT : Method B 19 13 Sensitivity factor, Y T , and relative notch sensitivity factor, Y rel T . 21 13.1 Basic uses . 21
11、13.2 Determination of the sensitivity factors . 21 13.3 Relative notch sensitivity factor, Y rel T : Method B. 22 14 Surface factors, Y R , Y RT , and relative surface factor, Y R rel T27 14.1 Influence of surface condition. 27 BS ISO 6336-3:2006iv 14.2 Determination of surface factors and relative
12、surface factors. 28 14.3 Relative surface factor, Y R rel T : Method B 28 15 Size factor, Y X30 15.1 Size factor, Y X : Method A . 30 15.2 Size factor, Y X : Method B . 30 Annex A (normative) Permissible bending stress, FP , obtained from notched, flat or plain polished test pieces 33 Annex B (infor
13、mative) Guide values for mean stress influence factor, Y M . 40 Bibliography . 42 BS ISO 6336-3:2006v Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normall
14、y 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 represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the
15、work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare In
16、ternational Standards. Draft International Standards adopted by the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of
17、 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 prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity calculation. This second edition cancels and replaces
18、 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 also incorporates the Technical Corrigendum ISO 6336-3:1996/Cor.1:1999. ISO 6336 consists of the following parts, under the general title
19、 Calculation of load capacity of spur and helical gears: Part 1: Basic principles, introduction and general influence factors Part 2: Calculation of surface durability (pitting) Part 3: Calculation of tooth bending strength Part 5: Strength and quality of materials Part 6: Calculation of service lif
20、e 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 the permissible bending stress for the material, is the basis for rating the bending strength of gear teeth. The stress occurs in the “ten
21、sion 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 generated, i.e. in the “compression fillets”, which are those of the non-working flanks. When the tooth loading is unidirectional and the teet
22、h 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 fillets. The endurable tooth loading of teeth subjected to a reversal of loading during each revolution, such as “idler gears”, is less t
23、han 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 loaded flanks. This is taken into consideration when determing permissible stresses (see ISO 6336-5). When gear rims are thin and tooth
24、spaces adjacent to the root surface narrow (conditions which can particularly apply to some internal gears), initial cracks commonly occur in the compression fillet. Since, in such circumstances, gear rims themselves can suffer fatigue breakage, special studies are necessary. See Clause 1. Several m
25、ethods for calculating the critical tooth root stress and evaluating some of the relevant factors have been approved. See ISO 6336-1. BS ISO 6336-3:20061 Calculation of load capacity of spur and helical gears Part 3: Calculation of tooth bending strength IMPORTANT The user of this part of ISO 6336 i
26、s 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 Method A. 1 Scope This part of ISO 6336 specifies the fundamental formulae for use in tooth bending stress calculations for involute ext
27、ernal or internal spur and helical gears with a rim thickness s R 0,5 h tfor external gears and s R 1,75 m nfor internal gears. In service, internal gears can experience failure modes other than tooth bending fatigue, i.e. fractures starting at the root diameter and progressing radially outward. Thi
28、s 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 as they are the result of loads transmitted by the gears and in so far as they can be evaluated quantitatively. The given formulae ar
29、e 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 basic racks if the virtual contact ratio nis less than 2,5. The load capacity determined on the basis of permissible bending stress is t
30、ermed “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 following referenced documents are indispensable for the application of this document. For dated references, only the edition cited
31、applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 53:1998, Cylindrical gears for general and heavy engineering Standard basic rack tooth profile ISO 1122-1:1998, Vocabulary of gear terms Part 1: Definitions related to geometry ISO
32、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 load capacity of spur and helical gears Part 5: Strength and quality of material 3 Terms, definitions, symbols and abbreviated term
33、s 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 breakage and safety factors Tooth breakage usually ends the service live of a transmission. Sometimes, the destruction of all gears in a tr
34、ansmission 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 chosen value of the safety factor S Fagainst tooth breakage should be larger than the safety factor against pitting. General comments
35、 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 safety factor. This part of ISO 6336 does not apply at stress levels above those permissible for 10 3cycles, since stresses in this r
36、ange 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 separately for pinion and wheel; Fshall be less than FP . 5.1 Safety factor for bending strength (safety against tooth breakage),
37、S FCalculate S Fseparately for pinion and wheel: FG1 F1 F min F1 SS = W (1) FG2 F2 Fmin F2 SS = W (2) F1and F2are derived from Equations (3) and (4). The values of FGfor reference stress and static stress are calculated in accordance with 5.3.2.1 and 5.3.2.2, using Equation (5). For limited life, FG
38、is 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 method used for each value shall be stated in the calculation report. NOTE Safety factors in accordance with the prese
39、nt 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, FTooth root stress Fis the maximum tensile stress at the surface in the root. 5.2.1 Method A In principle, the maximum
40、tensile stress can be determined by any appropriate method (finite element analysis, integral equations, conformal mapping procedures or experimentally by strain measurement, etc.). In order to determine the maximum tooth root stress, the effects of load distribution over two or more engaging teeth
41、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 justifiable in such cases. BS ISO 6336-3:20063 5.2.2 Method B According to this part of ISO 6336, the local tooth root stre
42、ss 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 application of load at the outer point of single pair tooth contact of spur gears or of the virtual spur gears of he
43、lical 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 virtual contact ratios in the range 2 u n 2,5, it is assumed that the determinant stress occurs with application of load
44、 at the inner point of triple pair tooth contact. In ISO 6336, this assumption is taken into consideration by the deep tooth factor, Y DT.In the case of helical gears, the factor, Y , accounts for deviations from these assumptions. Method B is suitable for general calculations and is also appropriat
45、e for computer programming and for the analysis of pulsator tests (with a given point of application of loading). The total tangential load in the case of gear trains with multiple transmission paths (planetary gear trains, split-path gear trains) is not quite evenly distributed over the individual
46、meshes (depending on design, tangential speed and manufacturing accuracy). This is to be taken into consideration by inserting a mesh load factor, K , to follow K Ain Equation (3), in order to adjust as necessary the average load per mesh. FF 0AvFFKKKK = (3) where F0is the nominal tooth root stress,
47、 which is the maximum local principal stress produced at the tooth root when an error-free gear pair is loaded by the static nominal torque and without any pre-stress such as shrink fitting, i.e. stress ratio R = 0 see Equation (4); FPis the permissible bending stress (see 5.3); K Ais the applicatio
48、n factor (see ISO 6336-6), which takes into account load increments due to externally influenced variations of input or output torque; K vis the dynamic factor (see ISO 6336-1), which takes into account load increments due to internal dynamic effects; K Fis the face load factor for tooth root stress
49、 (see ISO 6336-1), which takes into account uneven distribution of load over the facewidth due to mesh-misalignment caused by inaccuracies in manufacture, elastic deformations, etc.; K Fis the transverse load factor for tooth root stress (see ISO 6336-1), which takes into account uneven load distribution in the transverse direction, resulting, for example, from pitch devia
