INDIAN REGISTER OF SHIPPING CLASSIFICATION NOTES

Transcription

1 INDIAN REGISTER OF SHIPPING CLASSIFICATION NOTES Marine Gears Calculation of Loa Capacity of Involute Parallel Axis Spur an Helical Gears January 05

2 January 05 Page of 9 CLASSIFICATION NOTES Marine Gears Calculation of Loa Capacity of Involute Parallel Axis Spur an Helical Gears (This ocument is applicable to any marine gear subject to approval an to any type approve marine gear from the ate of the first renewal after January 05. For a Marine gear approve prior to January 05 where no failure has occurre an no changes in esign/scantlings of the gear meshes or materials or eclare loa capacity ata has taken place the requirements of this classification note may be waive.) January, 05

3 January 05 Page 3 of 9 Marine Gears Calculation of Loa Capacity of Involute Parallel Axis Spur an Helical Gears Contents Section Basic Principles Introuction an General Influence Factors Surface Durability (Pitting) 3 Tooth Root Bening Strength

4 January 05 Page 4 of 9 Section Basic Principles Introuction an General Influence Factors. Introuction.. The following efinitions are mainly base on the ISO 6336 stanar (hereinafter calle reference stanar ) for the calculation of loa capacity of spur an helical gears.. Scope an fiel of application.. The following requirements apply to enclose gears, both intene for main propulsion an for essential auxiliary services, which accumulate a large number of loa cycles (several millions), as require by the rules... The following requirements eal with the etermination of loa capacity of external an internal involute spur an helical gears, having parallel axis, with regar to surface urability (pitting) an tooth root bening strength an to this purpose the relevant basic equations are provie in Sec an Sec The influence factors common to sai equations in Sec an Sec 3 are escribe in this section...4 The others, introuce in connection with each basic equation, are escribe in the following Parts an All influence factors are efine regaring their physical interpretation. Some of the influence factors are etermine by the gear geometry or have been establishe by conventions. These factors are to be calculate in accorance with the equations provie. Other factors, which are approximations, may be calculate accoring to methos acceptable to IRS..3 Symbols an units.3. The main symbols use are liste below..3. Other symbols introuce in connection with the efinition of influence factors are escribe in the appropriate sections. SI units have been aopte. a centre istance mm b common face with mm b, face with of pinion, wheel mm

5 January 05 Page 5 of 9 reference iameter mm, reference iameter of pinion, wheel mm a, tip iameter of pinion, wheel mm b, base iameter of pinion, wheel mm f, root iameter of pinion, wheel mm w, working iameter of pinion, wheel mm Ft nominal tangential loa N Fbt nominal tangential loa on base cyliner in the transverse section N h tooth epth mm mn normal moule mm mt transverse moule mm n, rotational spee of pinion, wheel revs/min (rpm) P maximum continuous power transmitte by the gear set kw T, torque in way of pinion, wheel Nm u gear ratio v linear velocity at pitch iameter m/s x, aenum moification coefficient of pinion, wheel number of teeth, number of teeth of pinion, wheel virtual number of teeth n αn normal pressure angle at reference cyliner αt transverse pressure angle at ref. cyliner αtw transverse pressure angle at working pitch cyliner β helix angle at reference cyliner βb helix angle at base cyliner εα transverse contact ratio εβ overlap ratio total contact ratio εγ.4 Geometrical efinitions.4. For internal gearing, a,,a, b an w are negative. The pinion is efine as the gear with the smaller number of teeth, therefore the absolute value of the gear ratio, efine as follows, is always greater or equal to the unity: u=/ =w/w =/.4. For external gears u is positive, for internal gears u is negative.

6 January 05 Page 6 of In the equation of surface urability b is the common face with on the pitch iameter..4.4 In the equation of tooth root bening stress b or b are the face withs at the respective tooth roots. In any case, b an b are not to be taken as greater than b by more than one moule (mn) on either sie..4.5 The common face with b may be use also in the equation of teeth root bening stress if significant crowning or en relief have been aopte. tan t tan n cos tan tan cos b t, m, n cos b,, cos t w w a u au u where a 0.5 w w n, cos, b cos m t m n cos inv tan 80 ; α [ ] inv x x inv tan or tw t n c os tw m t a cos t 0.5 a b 0.5 m t a cos t b a sin the positive sign is use for external gears, the negative sign for internal gears tw b sin m n

7 January 05 Page 7 of 9 for ouble helix, b is to be taken as the with of one helix v 3 n / 60 0,,.5 Nominal tangential loa, Ft.5. The nominal tangential loa, Ft, tangential to the reference cyliner an perpenicular to the relevant axial plane, is calculate irectly from the maximum continuous power transmitte by the gear set by means of the following equations: T, 30 0 n 3, P F t 000 T /,,.6 General influence factors.6. Application factor, A ) a) The application factor, A, accounts for ynamic overloas from sources external to the gearing. b) Where the vessel, on which the reuction gear is being use, is receiving an Ice Class notation, the Application Factor or the Nominal Tangential Force shoul be ajuste to reflect the ice loa associate with the contemplate ice class notation. c) A, for gears esigne for infinite life is efine as the ratio between the maximum repetitive cyclic torque applie to the gear set an the nominal rate torque. ) The nominal rate torque is efine by the rate power an spee an is the torque use in the rating calculations. e) The factor mainly epens on: characteristics of riving an riven machines; ratio of masses; type of couplings; operating conitions (overspees, changes in propeller loa conitions, etc.). When operating near a critical spee of the rive system, a careful analysis of conitions must be mae. f) The application factor, A, shoul be etermine by measurements or by system analysis acceptable to the Society. Where a value etermine in such a way cannot be supplie, the following values can be consiere.

8 January 05 Page 8 of 9 Main propulsion iesel engine with hyraulic or electromagnetic slip coupling iesel engine with high elasticity coupling iesel engine with other couplings Auxiliary gears electric motor, iesel engine with hyraulic or electromagnetic slip coupling iesel engine with high elasticity coupling iesel engine with other couplings Loa sharing factor, γ a) The loa sharing factor, γ accounts for the malistribution of loa in multiple path transmissions (ual tanem, epicyclic, ouble helix, etc.) b) γ is efine as the ratio between the maximum loa through an actual path an the evenly share loa. The factor mainly epens on accuracy an flexibility of the branches. c) The loa sharing factor, γ, shoul be etermine by measurements or by system analysis. Where a value etermine in such a way cannot be supplie, the following values can be consiere for epicyclic gears: up to 3 planetary gears.00 4 planetary gears.0 5 planetary gears.30 6 planetary gears an over Internal ynamic factor, v a) The internal ynamic factor, v, accounts for internally generate ynamic loas ue to vibrations of pinion an wheel against each other. b) v is efine as the ratio between the maximum loa which ynamically acts on the tooth flanks an the maximum externally applie loa (FtAγ). c) The factor mainly epens on: transmission errors (epening on pitch an profile errors); masses of pinion an wheel; gear mesh stiffness variation as the gear teeth pass through the meshing cycle; transmitte loa incluing application factor; pitch line velocity;

9 January 05 Page 9 of 9 ynamic unbalance of gears an shaft; shaft an bearing stiffnesses; amping characteristics of the gear system. ) The metho of calculation of internal ynamic factor, v, given herein may be applie only to cases where all the following conitions are satisfie: running velocity in the subcritical range, i.e.: v 00 u u 0 m/s spur gears an helical gears with 30 0 pinion with relatively low number of teeth, < 50 soli isc wheels or heavy steel gear rim This metho may be applie to all types of gears if v 00 u u 3 m/s, as well as to helical gears where 30. e) For gears other than the above, reference is to be mae to Metho B outline in the reference stanar ISO f) For spur gears an for helical gears with overlap ratio εβ v F t A b v 00 3 u u If AFt/b is less than 00 N/mm, this value is assume to be equal to 00 N/mm. Numerical values for the factor are to be as specifie in the Table.6.3 Table.6.3 Values of the factor for the calculation of v ISO accuracy graes ( See note) spur gears helical gears Note: ISO accuracy graes accoring to ISO 38. In case of mating gears with ifferent accuracy graes, the grae corresponing to the lower accuracy shoul be use.

10 January 05 Page 0 of 9 For all accuracy graes the factor is to be in accorance with the following: - for spur gears, = for helical gears, = Factor 3 is to be in accorance with the following: v If 0. then u u 3 v If u u v then u u g) For helical gears with overlap ratio εβ< the value v is etermine by linear interpolation between values etermine for spur gears (vα) an helical gears (vβ) in accorance with: v v v v Where: vα is the v value for spur gears, in accorance with f); vβ is the v value for helical gears, in accorance with f)..6.4 Face loa istribution factors, Hβ an Fβ a) The face loa istribution factors, Hβ for contact stress, Fβ for tooth root bening stress, account for the effects of non-uniform istribution of loa across the face with. b) Hβ is efine as follows: H maximum loa per unit face with mean loa per unit face with c) Fβ is efine as follows: F maximum mean bening stress at tooth root per unit face with bening stress at tooth roo per unit face with ) The mean bening stress at tooth root relates to the consiere face with b resp. b. Fβ can be expresse as a function of the factor Hβ.

11 January 05 Page of 9 e) The factors Hβ an Fβ mainly epen on: gear tooth manufacturing accuracy; errors in mounting ue to bore errors; bearing clearances; wheel an pinion shaft alignment errors; elastic eflections of gear elements, shafts, bearings, housing an founations which support the gear elements; thermal expansion an istortion ue to operating temperature; compensating esign elements (tooth crowning, en relief, etc.). f) The face loa istribution factors, Hβ for contact stress, an Fβ for tooth root bening stress, are to be etermine accoring to the Metho C outline in the reference stanar ISO Alternative methos acceptable to IRS may be applie. In case the harest contact is at the en of the face with Fβ is given by the following equations: N F H N b / h b / h b / h (b/h) = face with/tooth height ratio, the minimum of b/h or b/h. For ouble helical gears, the face with of only one helix is to be use. When b/h<3 the value b/h=3 is to be use. In case of gears where the ens of the face with are lightly loae or unloae (en relief or crowning): F H.6.5 Transverse loa istribution factors, Hα an Fα a) The transverse loa istribution factors, Hα for contact stress an Fα for tooth root bening stress, account for the effects of pitch an profile errors on the transversal loa istribution between two or more pairs of teeth in mesh.

12 January 05 Page of 9 b) The factors Hα an Fα mainly epen on: total mesh stiffness; total tangential loa Ft, A, γ, v, Hβ; base pitch error; tip relief; running-in allowances. c) The transverse loa istribution factors, Hα for contact stress an Fα for tooth root bening stress, are to be etermine accoring to Metho B outline in the reference stanar ISO

13 January 05 Page 3 of 9 Section Surface Durability (Pitting). Scope an general remarks.. The criterion for surface urability is base on the Hert pressure on the operating pitch point or at the inner point of single pair contact. The contact stress σh must be equal to or less than the permissible contact stress σhp.. Basic equations.. Contact stress H H 0 A v H H HP where: σh0 = basic value of contact stress for pinion an wheel F u t for pinion H 0 B H E b u where: F u t for wheel H 0 D H E b u B = single pair tooth contact factor for pinion (see.3) D = single pair tooth contact factor for wheel (see.3) H = one factor (see.4) E = elasticity factor (see.5) ε = contact ratio factor (see.6) β = helix angle factor (see.7) Ft ) = nominal tangential loa at reference cyliner in the transverse section (see Section

14 January 05 Page 4 of 9 b u = common face with = reference iameter of pinion = gear ratio (for external gears u is positive, for internal gears u is negative) Regaring factors A, γ, v, Hα an Hβ, see Section... Permissible contact stress... The permissible contact stress σhp is to be evaluate separately for pinion an wheel: HP H lim S H N L v R W X where: σhlim = enurance limit for contact stress (see.8) N = life factor for contact stress (see.9) L = lubrication factor (see.0) v = velocity factor (see.0) R = roughness factor (see.0) W = harness ratio factor (see.) X = sie factor for contact stress (see.) SH = safety factor for contact stress (see.3).3 Single pair tooth contact factors, B an D.3. The single pair tooth contact factors, B for pinion an D for wheel, account for the influence of the tooth flank curvature on contact stresses at the inner point of single pair contact in relation to H..3. The factors transform the contact stresses etermine at the pitch point to contact stresses consiering the flank curvature at the inner point of single pair contact..3.3 The single pair tooth contact factors, B for pinions an D for wheels, are to be etermine as follows:

15 January 05 Page 5 of 9 For spur gears, =0 B = M or whichever is the larger value D = M or whichever is the larger value tan M b a b a tw tan M b a b a tw For helical gears when B = D =.3.4 For helical gears when < the values of B an D are etermine by linear interpolation between B an D for spur gears an B an D for helical gears having. Thus: an B B M M an D D M M For internal gears, D shall be taken as equal to..4 one factor, H.4. The one factor, H, accounts for the influence on the Hertian pressure of tooth flank curvature at pitch point an transforms the tangential loa at the reference cyliner to the normal loa at the pitch cyliner..4. The one factor, H, is to be calculate as follows: tw t b H tan cos cos

16 January 05 Page 6 of 9.5 Elasticity factor, E.5. The elasticity factor, E, accounts for the influence of the material properties E (moulus of elasticity) an ν (Poisson s ratio) on the contact stress..5. The elasticity factor, E, for steel gears (E= N/mm, ν= 0.3) is equal to: E = 89.8 N/mm.5.3 In other cases, reference is to be mae to the reference stanar ISO Contact ratio factor, ε.6. The contact ratio factor, ε, accounts for the influence of the transverse contact ratio an the overlap ratio on the specific surface loa of gears..6. The contact ratio factor, ε, is to be calculate as follows: Spur gears: 4 3 Helical gears: - for εβ < for εβ.7 Helix angle factor, β.7. The helix angle factor, β, accounts for the influence of helix angle on surface urability, allowing for such variables as the istribution of loa along the lines of contact. β is epenent only on the helix angle.

17 January 05 Page 7 of 9.7. The helix angle factor, β, is to be calculate as follows: cos Where β is the reference helix angle..8 Enurance limit for contact stress, σhlim.8. For a given material, σhlim is the limit of repeate contact stress which can be permanently enure. The value of σhlim can be regare as the level of contact stress which the material will enure without pitting for at least 5x0 7 loa cycles..8. For this purpose, pitting is efine by: - for not surface harene gears: pitte area > % of total active flank area - for surface harene gears: pitte area > 0,5% of total active flank area, or > 4% of one particular tooth flank area..8.3 The σhlim values are to correspon to a failure probability of % or less..8.4 The enurance limit mainly epens on: - material composition, cleanliness an efects; - mechanical properties; - resiual stresses; - harening process, epth of harene one, harness graient; - material structure (forge, rolle bar, cast)..8.5 The enurance limit for contact stress σhlim, is to be etermine, in general, making reference to values inicate in the stanar ISO , for material quality MQ..9 Life factor, N.9. The life factor N, accounts for the higher permissible contact stress in case a limite life (number of cycles) is require..9. The factor mainly epens on: - material an heat treatment; - number of cycles; - influence factors (R, v, L, W, X)..9.3 The life factor, N, is to be etermine accoring to Metho B outline in the reference stanar ISO

18 January 05 Page 8 of 9.0 Influence factors of lubrication film on contact stress, L, v an R.0. The lubricant factor, L, accounts for the influence of the type of lubricant an its viscosity. The velocity factor, v, accounts for the influence of the pitch line velocity. The roughness factor, R, accounts for the influence of the surface roughness on the surface enurance capacity..0. The factors may be etermine for the softer material where gear pairs are of ifferent harness..0.3 The factors mainly epen on: - viscosity of lubricant in the contact one; - the sum of the instantaneous velocities of the tooth surfaces; - loa; - relative raius of curvature at the pitch point; - surface roughness of teeth flanks; - harness of pinion an gear..0.4 The lubricant factor, L, the velocity factor, v, an the roughness factor R are to be calculate as follows: a) Lubricant factor, L The factor, L, is to be calculate from the following equation: L C L 4 C L In the range 850 N/mm 00 N/mm, H lim CL is to be calculate as follows: C L 0.08 H lim If σhlim < 850 N/mm, take CL = 0.83 If σhlim > 00 N/mm, take CL = 0.9 Where: ν40 = nominal kinematic viscosity of the oil at 40 C, mm /s b) Velocity factor, v The velocity factor, v, is to be calculate from the following equations:

19 January 05 Page 9 of 9 v C V C V v In the range 850 N/mm σhlim 00 N/mm, CV is to be calculate as follows: C V C L 0.0 c) Roughness factor, R The roughness factor, R, is to be calculate from the following equations: Where: R 3 R 0 C R R R R The peak-to-valley roughness etermine for the pinion R an for the wheel R are mean values for the peak-to-valley roughness R measure on several tooth flanks (R as efine in the reference stanar ISO 6336-). R 3 R 0 0 re relative raius of curvature: re Wherein: 0.5, b, tan tw (also for internal gears, b negative sign) If the roughness state is an arithmetic mean roughness, i.e. Ra value (=CLA value) (=AA value) the following approximate relationship can be applie: R CLA AA a R 6

20 January 05 Page 0 of 9 In the range 850 N/mm σhlim 00 N/mm, CR is to be calculate as follows: C R H lim If σhlim < 850 N/mm, take CR = 0.50 If σhlim > 00 N/mm, take CR = Harness ratio factor, W.. The harness ratio factor, W, accounts for the increase of surface urability of a soft steel gear meshing with a significantly harer gear with a smooth surface in the following cases: a) Surface-harene pinion with through-harene wheel If HB< 30 W 3. R H 0.5 If 30 HB 470 W. HB R H 0.5 If HB >470 W 3 R H 0.5 Where: pair HB = Brinell harness of the tooth flanks of the softer gear of the RH = equivalent roughness, μm R H R / R / R re v / ρre = relative raius of curvature (see clause.0 c) b) Through-harene pinion an wheel When the pinion is substantially harer than the wheel, the work harening effect increases the loa capacity of the wheel flanks. W applies to the wheel only, not to the pinion. If HB/HB <. W

21 January 05 Page of 9 If. HB/HB u If HB/HB> u W W If gear ratio u>0 then the value u=0 is to be use. In any case, if calculate W < then the value W =.0 is to be use. HB HB. Sie factor, X.. The sie factor, X, accounts for the influence of tooth imensions on permissible contact stress an reflects the non-uniformity of material properties... The factor mainly epens on: - material an heat treatment; - tooth an gear imensions; - ratio of case epth to tooth sie; - ratio of case epth to equivalent raius of curvature...3 For through-harene gears an for surface-harene gears with aequate caseepth relative to tooth sie an raius of relative curvature X =. When the caseepth is relatively shallow then a smaller value of X shoul be chosen..3 Safety factor for contact stress, SH.3. The safety factor for contact stress, SH, can be assume by the Society taking into account the type of application. The following guiance values can be aopte: - Main propulsion gears:.0 to.40 - Auxiliary gears:.5 to.0.3. For gearing of uplicate inepenent propulsion or auxiliary machinery, uplicate beyon that require for class, a reuce value can be assume at the iscretion of the IRS.

22 January 05 Page of 9 3. Scope an general remarks Section 3 Tooth Root Bening Strength 3.. The criterion for tooth root bening strength is the permissible limit of local tensile strength in the root fillet. The root stress σf an the permissible root stress σfp shall be calculate separately for the pinion an the wheel. 3.. σf must not excee σfp The following formulae an efinitions apply to gears having rim thickness greater than 3.5mn The result of rating calculations mae by following this metho are acceptable for normal pressure angles up to 5 an reference helix angles up to For larger pressure angles an large helix angles, the calculate results shoul be confirme by experience as by Metho A of the reference stanar ISO Basic equations 3.. Tooth root bening stress for pinion an wheel F F bm t n F S B DT A v F F FP where: F = tooth form factor (see clause 3.3) S = stress correction factor (see clause 3.4) β = helix angle factor (see clause 3.5) B = rim thickness factor (see clause 3.6) DT = eep tooth factor (see clause 3.7) F,,,,, (see Sec ) t A v F F b (see Sec, clause.4) mn (see Sec, clause.3)

23 January 05 Page 3 of Permissible tooth root bening stress for pinion an wheel FP FE S F N relt RrelT X where: σfe = bening enurance limit = esign factor N = life factor δrelt = relative notch sensitivity factor RrelT = relative surface factor X = sie factor = safety factor for tooth root bening stress SF 3.3 Tooth form factor, F 3.3. The tooth form factor, F, represents the influence on nominal bening stress of the tooth form with loa applie at the outer point of single pair tooth contact. F shall be etermine separately for the pinion an the wheel. In the case of helical gears, the form factors for gearing shall be etermine in the normal section, i.e. for the virtual spur gear with virtual number of teeth n The tooth form factor, F, is to be calculate as follows: Where: F h F 6 m s Fn m n n cos cos Fen n hf = bening moment arm for tooth root bening stress for application of loa at the outer point of single tooth pair contact mm sfn = tooth root normal chor in the critical section mm αfen = pressure angle at the outer point of single tooth pair contact in the normal section

24 January 05 Page 4 of 9 Fig. 3.3 : Dimensions of h F, s Fn an α Fen for external gear For the calculation of hf, sfn an αfen, the proceure outline in the reference stanar ISO (Metho B) is to be use. 3.4 Stress correction factor, S 3.4. The stress correction factor S, is use to convert the nominal bening stress to the local tooth root stress, taking into account that not only bening stresses arise at the root S applies to the loa application at the outer point of single tooth pair contact. S shall be etermine separately for the pinion an for the wheel. The stress correction factor, S, is to be etermine with the following equation (having range of valiity: q 8 ):..3 L. 0.3 L q S s s Where: q s s Fn F qs ρf L = notch parameter, = root fillet raius in the critical section, mm = sfn /hf For hf an sfn see clause 3. For the calculation of ρf the proceure outline in the reference stanar ISO is to be use.

25 January 05 Page 5 of Helix angle factor, β 3.5. The helix angle factor, β, converts the stress calculate for a point loae cantilever beam representing the substitute gear tooth to the stress inuce by a loa along an oblique loa line into a cantilever plate which represents a helical gear tooth The helix angle factor, β is to be calculate as follows: 0 where: β = reference helix angle in egrees. The value.0 is substitute for εβ when εβ >.0, an 30 is substitute for β > Rim thickness factor, B 3.6. The rim thickness factor, B, is a simplifie factor use to e-rate thin rimme gears. For critically loae applications, this metho shoul be replace by a more comprehensive analysis. Factor B is to be etermine as follows: a) for external gears: if / h. s R if 0.5 / h. where: B h s R.6 ln. 4 B s R sr = rim thickness of external gears, mm h = tooth height, mm The case s R / h 0. 5 is to be avoie. b) for internal gears: if / 3. 5 s R m n if.75 / m 3. 5 where: B s n.5 ln R n B s R sr = rim thickness of internal gears, mm The case s /. 75 is to be avoie. R m n m

26 January 05 Page 6 of Deep tooth factor, DT 3.7. The eep tooth factor, DT, ajusts the tooth root stress to take into account high precision gears an contact ratios within the range of virtual contact ratio.05. 5, where: n n cos b 3.7. Factor DT is to be etermine as follows: if ISO accuracy grae 4 an. 5 n if ISO accuracy grae 4 an DT n 0. 7 in all other cases. 0 n DT DT 3.8 Bening enurance limit, σfe 3.8. For a given material, σfe is the local tooth root stress which can be permanently enure Accoring to the reference stanar ISO the number of 3x0 6 cycles is regare as the beginning of the enurance limit σfe is efine as the uniirectional pulsating stress with a minimum stress of ero (isregaring resiual stresses ue to heat treatment). Other conitions such as alternating stress or prestressing etc. are covere by the esign factor The σfe values are to correspon to a failure probability % or less The enurance limit mainly epens on: - material composition, cleanliness an efects; - mechanical properties; - resiual stresses; - harening process, epth of harene one, harness graient; - material structure (forge, rolle bar, cast) The bening enurance limit, σfe is to be etermine, in general, making reference to values inicate in the reference stanar ISO , for material quality MQ. 3.9 Design factor, 3.9. The esign factor,, takes into account the influence of loa reversing an shrinkfit prestressing on the tooth root strength, relative to the tooth root strength with uniirectional loa as efine for σfe.

27 January 05 Page 7 of The esign factor,, for loa reversing, is to be etermine as follows: =.0 in general; = 0.9 for gears with occasional part loa in reverse irection, such as main wheel in reversing gearboxes; = 0.7 for iler gears 3.0 Life factor, N 3.0. The life factor, N, accounts for the higher tooth root bening stress permissible in case a limite life (number of cycles) is require The factor mainly epens on: - material an heat treatment; - number of loa cycles (service life); - influence factors (δrelt,rrelt, X) The life factor, N, is to be etermine accoring to Metho B outline in the reference stanar ISO Relative notch sensitivity factor, δrelt 3.. The relative notch sensitivity factor, δrelt, inicates the extent to which the theoretically concentrate stress lies above the fatigue enurance limit. The factor mainly epens on material an relative stress graient. 3.. The relative notch sensitivity factor, δrelt, is to be etermine as follows: relt 0. ' q. ' s where: qs = notch parameter (see clause 3.4) ρ = slip-layer thickness, mm, from the following table Material case harene steels, flame or inuction harene steels through-harene steels ), yiel point Re= ρ, mm N/mm² N/mm² N/mm² N/mm² nitrie steels ) The given values of ρ can be interpolate for values of Re not state above

28 January 05 Page 8 of 9 3. Relative surface factor, RrelT 3.. The relative surface factor, RrelT, takes into account the epenence of the root strength on the surface conition in the tooth root fillet, mainly the epenence on the peak to valley surface roughness. 3.. The relative surface factor, RrelT is to be etermine as follows: R R Material R R case harene steels, through - harene steels ( B 800 N/mm normalise steels ( B 800 N/mm R nitrie steels ) ) Where: R = mean peak-to-valley roughness of tooth root fillets, μm σb = tensile strength, N/mm 3..3 The metho applie here is only vali when scratches or similar efects eeper than R are not present If the roughness state is an arithmetic mean roughness, i.e. Ra value (=CLA value) (=AA value) the following approximate relationship can be applie: R CLA AA a R Sie factor, X 3.3. The sie factor, X, takes into account the ecrease of the strength with increasing sie The factor mainly epens on: - material an heat treatment; - tooth an gear imensions; - ratio of case epth to tooth sie.

29 January 05 Page 9 of The sie factor, X, is to be etermine as follows: X =.00 for mn 5 generally X = mn for 5 < mn < 30 normalise an through-harene X = 0.85 for mn 30 steels X = mn for 5 < mn < 5 X = 0.80 for mn 5 surface harene steels 3.4 Safety factor for tooth root bening stress, SF 3.4. The safety factor for tooth root bening stress, SF, can be assume by IRS taking into account the type of application The following guiance values can be aopte: - Main propulsion gears:.55 to.00 - Auxiliary gears:.40 to For gearing of uplicate inepenent propulsion or auxiliary machinery, uplicate beyon that require for class, a reuce value can be assume at the iscretion of the IRS.