Marine gears load capacity of involute parallel axis spur and helical gears

Transcription

1 (1990) (Rev / Corr. 1996) (Rev. Oct 013) (Rev.3 Oct 015) Marine gears loa capacity of involute parallel axis spur an helical gears.1 Basic principles - introuction an general influence factors.1.1 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..1. Scope an fiel of application These 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), whose gear set is intene to transmit a maximum continuous power equal to, or greater than: - 0 kw for gears intene for main propulsion kw for gears intene for essential auxiliary services These requirements, however, may be applie to the enclose gears, whose gear set is intene to transmit a maximum continuous power less than those specifie above at the request of the iniviual society. The following efinitions 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 Parts an 3. The influence factors common to sai equations are escribe in the present Part 1. The others, introuce in connection with each basic equation, are escribe in the following Parts an 3. Notes: 1. The requirements of UR Rev. are to be uniformly implemente from 1 January 015 by all IACS Societies to any marine gear subject to approval an to any Type Approve marine gear from the ate of the first renewal after 1 January 015. For a marine gear approve prior to 1 January 015 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 UR Rev. may be waive.. The requirements of UR Rev.3 are to be uniformly implemente from 1 January 017 by all IACS Societies to any marine gear subject to approval an to any Type Approve marine gear from the ate of the first renewal after 1 January 017. For a marine gear approve prior to 1 January 017 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 UR Rev.3 may be waive. Page 1 of 3 IACS Req. 1990/Rev.3 015

2 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, can be calculate accoring to methos acceptable to the Society..1.3 Symbols an units The main symbols use are liste below. 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 1, face with of pinion, wheel mm reference iameter mm 1, reference iameter of pinion, wheel mm a1, tip iameter of pinion, wheel mm b1, base iameter of pinion, wheel mm f1, root iameter of pinion, wheel mm w1, working iameter of pinion, wheel mm F t nominal tangential loa N F bt nominal tangential loa on base cyliner in the transverse section N h tooth epth mm m n normal moule mm m t transverse moule mm n 1, rotational spee of pinion, wheel revs/min (rpm) P maximum continuous power transmitte by the gear set kw T 1, torque in way of pinion, wheel Nm u gear ratio v linear velocity at pitch iameter m/s x 1, aenum moification coefficient of pinion, wheel z number of teeth z 1, number of teeth of pinion, wheel z n virtual number of teeth α n normal pressure angle at reference cyliner α t transverse pressure angle at ref. cyliner α tw transverse pressure angle at working pitch cyliner Page of 3 IACS Req. 1990/Rev.3 015

3 β helix angle at reference cyliner β b helix angle at base cyliner ε α ε β ε γ transverse contact ratio overlap ratio total contact ratio Page 3 of 3 IACS Req. 1990/Rev.3 015

4 .1.4 Geometrical efinitions For internal gearing z, 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: uz /z 1 w/ w1 / 1 For external gears u is positive, for internal gears u is negative. In the equation of surface urability b is the common face with on the pitch iameter. In the equation of tooth root bening stress b 1 or b are the face withs at the respective tooth roots. In any case, b 1 an b are not to be taken as greater than b by more than one moule (m n) on either sie. 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. tanα t tanα n cos β tan β tan β cos b α t 1, z 1,m n cos β b1, 1, cosα t w1 w a u + 1 au u + 1 where a 0.5 ( + ) w1 w z n1, z1, cos β cos β mn m t cos β b πα invα tanα ; α [ ] 180 inv + x 1 α tw invα t + tanα n or z1 + z x m ( z z ) t cosα + 1 tw a cosα t ε α a1 b1 a b 0,5 ± 0,5 a sinα tw π mt cosαt the positive sign is use for external gears, the negative sign for internal gears Page 4 of 3 IACS Req. 1990/Rev.3 015

5 b sin β ε β π mn for ouble helix, b is to be taken as the with of one helix ε ε + ε γ α β v π n 3 1, 1, / Nominal tangential loa, F t The nominal tangential loa, F t, 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 1, P π n 1, F t 000 T 1, / 1,.1.6 General influence factors Application factor, K A 1) The application factor, K A, accounts for ynamic overloas from sources external to the gearing. K 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. 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,...). When operating near a critical spee of the rive system, a careful analysis of conitions must be mae. The application factor, K 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. a) Main propulsion - iesel engine with hyraulic or electromagnetic slip coupling : iesel engine with high elasticity coupling : iesel engine with other couplings : ) 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 requeste Ice Class, i.e. applying the esign approach in UR I3 when applicable. Page 5 of 3 IACS Req. 1990/Rev.3 015

6 b) 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, K γ The loa sharing factor, K γ accounts for the malistribution of loa in multiple path transmissions (ual tanem, epicyclic, ouble helix, etc.) K 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. The loa sharing factor, K 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 : planetary gears : planetary gears : planetary gears an over : Internal ynamic factor, K v The internal ynamic factor, K v, accounts for internally generate ynamic loas ue to vibrations of pinion an wheel against each other. K v is efine as the ratio between the maximum loa which ynamically acts on the tooth flanks an the maximum externally applie loa (F tk AK γ). 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; - ynamic unbalance of gears an shaft; - shaft an bearing stiffnesses; - amping characteristics of the gear system. The ynamic factor, K v, is to be calculate as follows: This metho may be applie only to cases where all the following conitions are satisfie: - running velocity in the subcritical range, i.e.: vz1 u < 10 m/s u - spur gears ( β 0 ) an helical gears with β 30 - pinion with relatively low number of teeth, z 1< 50 - soli isc wheels or heavy steel gear rim Page 6 of 3 IACS Req. 1990/Rev.3 015

7 This metho may be applie to all types of gears if gears where β > 30. vz 100 u 1+ u 1 < 3 m/s, as well as to helical For gears other than the above, reference is to be mae to Metho B outline in the reference stanar ISO a) For spur gears an for helical gears with overlap ratio ε β 1 K 1 vz1 u Kv 1+ + K K3 Ft K u A b If K AF t/b is less than 100 N/mm, this value is assume to be equal to 100 N/mm. Numerical values for the factor K 1 are to be as specifie in the Table 1.1 K 1 ISO accuracy graes ) spur gears helical gears Table 1.1 Values of the factor K 1 for the calculation of K v For all accuracy graes the factor K is to be in accorance with the following: - for spur gears, K for helical gears, K Factor K 3 is to be in accorance with the following: vz1 u If 0. then K u vz1 u vz1 u If > 0. then K u u b) For helical gears with overlap ratio ε β<1 the value K v is etermine by linear interpolation between values etermine for spur gears (K vα) an helical gears (K vβ) in accorance with: Where: K v K ( K K ) vα ε β vα vβ K vα is the K v value for spur gears, in accorance with a); K vβ is the K v value for helical gears, in accorance with a). ) ISO accuracy graes accoring to ISO 138. In case of mating gears with ifferent accuracy graes, the grae corresponing to the lower accuracy shoul be use. Page 7 of 3 IACS Req. 1990/Rev.3 015

8 Face loa istribution factors, K Hβ an K Fβ The face loa istribution factors, K Hβ for contact stress, K Fβ for tooth root bening stress, account for the effects of non-uniform istribution of loa across the face with. K Hβ is efine as follows: K Hβ maximum loaper unit face with mean loa per unit face with K Fβ is efine as follows: K Fβ maximum bening stress at tooth root per unit face with mean bening stress at tooth roo per unit face with The mean bening stress at tooth root relates to the consiere face with b 1 resp. b. K Fβ can be expresse as a function of the factor K Hβ. The factors K Hβ an K 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.). The face loa istribution factors, K Hβ for contact stress, an K 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 the Society may be applie. a) In case the harest contact is at the en of the face with K Fβ is given by the following equations: K N Fβ K H β N 1+ ( b / h) ( b / h) + ( b / h) (b/h) face with/tooth height ratio, the minimum of b 1/h 1 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/h3 is to be use. b) In case of gears where the ens of the face with are lightly loae or unloae (en relief or crowning): K K Fβ Hβ Page 8 of 3 IACS Req. 1990/Rev.3 015

9 Transverse loa istribution factors, K Hα an K Fα The transverse loa istribution factors, K Hα for contact stress an K 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. The factors K Hα an K Fα mainly epen on: - total mesh stiffness; - total tangential loa F t, K A, K γ, K v, K Hβ; - base pitch error; - tip relief; - running-in allowances. The transverse loa istribution factors, K Hα for contact stress an K Fα for tooth root bening stress, are to be etermine accoring to Metho B outline in the reference stanar ISO Surface urability (pitting)..1 Scope an general remarks The criterion for surface urability is base on the Hertz pressure on the operating pitch point or at the inner point of single pair contact. The contact stress σ H must be equal to or less than the permissible contact stress σ HP... Basic equations...1 Contact stress σ H σ H0 K A K γ K v K Hα K Hβ σ HP where: σ H0 basic value of contact stress for pinion an wheel ( u + 1) Ft σ H 0 B H E ε β for pinion b u 1 where: ( u + 1) Ft σ H 0 D H E ε β for wheel b u 1 B single pair tooth contact factor for pinion (see clause.3) D single pair tooth contact factor for wheel (see clause.3) H zone factor (see clause.4) E elasticity factor (see clause.5) Page 9 of 3 IACS Req. 1990/Rev.3 015

10 ε contact ratio factor (see clause.6) β helix angle factor (see clause.7) F t b 1 u nominal tangential loa at reference cyliner in the transverse section (see Part 1) common face with reference iameter of pinion gear ratio (for external gears u is positive, for internal gears u is negative) Regaring factors K A, K γ, K v, K Hα an K Hβ, see Part Permissible contact stress The permissible contact stress σ HP is to be evaluate separately for pinion an wheel: σ HP σ S H lim H N L v R W X where: σ Hlim enurance limit for contact stress (see clause.8) N life factor for contact stress (see clause.9) L lubrication factor (see clause.10) v velocity factor (see clause.10) R roughness factor (see clause.10) W harness ratio factor (see clause.11) X size factor for contact stress (see clause.1) S H safety factor for contact stress (see clause.13)..3 Single pair tooth contact factors, B an D 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. 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. The single pair tooth contact factors, B for pinions an D for wheels, are to be etermine as follows: Page 10 of 3 IACS Req. 1990/Rev.3 015

11 For spur gears, ε β0 B M 1 or 1 whichever is the larger value D M or 1 whichever is the larger value M 1 a1 b1 π 1 z 1 tanα tw a b 1 ( ε 1) α π z M a b π 1 z tanα tw a1 b1 1 ( ε 1) α π z 1 For helical gears when ε β 1 B 1 D 1 For helical gears when ε β <1 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 ε β 1. Thus: B D ( M1 1) an 1 ( M 1) an 1 M1 ε β B M ε β D For internal gears, D shall be taken as equal to one factor, H The zone factor, H, accounts for the influence on the Hertzian 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. The zone factor, H, is to be calculate as follows: H cos βb cos α tanα t tw Page 11 of 3 IACS Req. 1990/Rev.3 015

12 ..5 Elasticity factor, E 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. The elasticity factor, E, for steel gears (E N/mm, ν 0.3) is equal to: E N/mm In other cases, reference is to be mae to the reference stanar ISO Contact ratio factor, ε 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. The contact ratio factor, ε, is to be calculate as follows: Spur gears: ε 4 α ε 3 Helical gears: - for ε β <1 4 ε 3 α ε 1 ( ε ) β ε + ε β α - for ε β 1 ε 1 ε α..7 Helix angle factor, β 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. The helix angle factor, β, is to be calculate as follows: β 1 cos β Where β is the reference helix angle. Page 1 of 3 IACS Req. 1990/Rev.3 015

13 ..8 Enurance limit for contact stress, σ Hlim For a given material, σ Hlim is the limit of repeate contact stress which can be permanently enure. The value of σ Hlim can be regare as the level of contact stress which the material will enure without pitting for at least 5x10 7 loa cycles. 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. The σ Hlim values are to correspon to a failure probability of 1% or less. The enurance limit mainly epens on: - material composition, cleanliness an efects; - mechanical properties; - resiual stresses; - harening process, epth of harene zone, harness graient; - material structure (forge, rolle bar, cast). The enurance limit for contact stress σ Hlim, is to be etermine, in general, making reference to values inicate in the stanar ISO , for material quality MQ...9 Life factor, N The life factor N, accounts for the higher permissible contact stress in case a limite life (number of cycles) is require. The factor mainly epens on: - material an heat treatment; - number of cycles; - influence factors ( R, v, L, W, X). The life factor, N, is to be etermine accoring to Metho B outline in the reference stanar ISO Influence factors of lubrication film on contact stress, L, v an R 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. The factors may be etermine for the softer material where gear pairs are of ifferent harness. The factors mainly epen on: - viscosity of lubricant in the contact zone; - the sum of the instantaneous velocities of the tooth surfaces; - loa; - relative raius of curvature at the pitch point; - surface roughness of teeth flanks; Page 13 of 3 IACS Req. 1990/Rev.3 015

14 - harness of pinion an gear. 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 ( C ) 4 1 L ν 40 In the range 850 N/mm σ H lim 100 N/mm, C L is to be calculate as follows: C L σ lim H If σ Hlim < 850 N/mm, take C L 0.83 If σ Hlim > 100 N/mm, take C L 0.91 Where: ν 40 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: v C V + ( C ) 1 V v In the range 850 N/mm σ Hlim 100 N/mm, C V is to be calculate as follows: C V C L c) Roughness factor, R The roughness factor, R, is to be calculate from the following equations: Where: R 3 R z10 C R R R z + R z1 z Page 14 of 3 IACS Req. 1990/Rev.3 015

15 The peak-to-valley roughness etermine for the pinion R z1 an for the wheel R z are mean values for the peak-to-valley roughness R z measure on several tooth flanks (R z as efine in the reference stanar ISO 6336-). R z 10 R 3 10 ρ re relative raius of curvature: ρ re ρ1 ρ ρ + ρ 1 Wherein: ρ 1, 0.5 b1, tanα tw (also for internal gears, b negative sign) If the roughness state is an arithmetic mean roughness, i.e. R a value (CLA value) (AA value) the following approximate relationship can be applie: R CLA AA a R z 6 In the range 850 N/mm σ Hlim 100 N/mm, C R is to be calculate as follows: CR σ H lim If σ Hlim < 850 N/mm, take C R If σ Hlim > 100 N/mm, take C R 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< 130 If 130 HB 470 If HB >470 Where: W W W 1 3. RzH HB RzH 3 R zh HB Brinell harness of the tooth flanks of the softer gear of the pair Page 15 of 3 IACS Req. 1990/Rev.3 015

16 R zh equivalent roughness, μm R zh R z ( 10 / ρre ) ( Rz1 / Rz ) ( v ν /1500) ρ re relative raius of curvature (see clause.10 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 1/HB < 1. 1 W HB HB u 1 1 If 1. HB 1/HB ( u 1) W W If HB 1/HB >1.7 ( ) If gear ratio u>0 then the value u0 is to be use. In any case, if calculate W <1 then the value W 1.0 is to be use...1 Size factor, X The size 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 size; - ratio of case epth to equivalent raius of curvature. For through-harene gears an for surface-harene gears with aequate caseepth relative to tooth size an raius of relative curvature X 1. When the caseepth is relatively shallow then a smaller value of X shoul be chosen...13 Safety factor for contact stress, S H The safety factor for contact stress, S H, can be assume by the Society taking into account the type of application. The following guiance values can be aopte: - Main propulsion gears: 1.0 to Auxiliary gears: 1.15 to 1.0 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 Society. Page 16 of 3 IACS Req. 1990/Rev.3 015

17 .3 Tooth root bening strength.3.1 Scope an general remarks The criterion for tooth root bening strength is the permissible limit of local tensile strength in the root fillet. The root stress σ F an the permissible root stress σ FP shall be calculate separately for the pinion an the wheel. σ F must not excee σ FP. The following formulae an efinitions apply to gears having rim thickness greater than 3.5m n. 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 30. 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..1 Tooth root bening stress for pinion an wheel σ F Ft bm n Y Y Y Y Y F S β B DT K A K γ K v K Fα K Fβ σ FP where: Y F tooth form factor (see clause 3.3) Y S stress correction factor (see clause 3.4) Y β helix angle factor (see clause 3.5) Y B rim thickness factor (see clause 3.6) Y DT eep tooth factor (see clause 3.7) F t, K A, Kγ, Kv, KFα, KFβ (see Part 1) b (see Part 1, clause 1.4) m n (see Part 1, clause 1.3).3.. Permissible tooth root bening stress for pinion an wheel where: σ FE Y Y N σ FEYY σ FP S F N Y δrelt Y RrelT bening enurance limit esign factor life factor Y δrelt relative notch sensitivity factor Y RrelT relative surface factor Y X size factor safety factor for tooth root bening stress S F Y X Page 17 of 3 IACS Req. 1990/Rev.3 015

18 .3.3 Tooth form factor, Y F The tooth form factor, Y F, represents the influence on nominal bening stress of the tooth form with loa applie at the outer point of single pair tooth contact. Y 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, Y F, is to be calculate as follows: hf 6 cosα Fen m n YF s Fn cosα n m n Where: h F bening moment arm for tooth root bening stress for application of loa at the outer point of single tooth pair contact mm s Fn tooth root normal chor in the critical section mm α Fen pressure angle at the outer point of single tooth pair contact in the normal section Fig. 3.1 Dimensions of h F, s Fn an α Fen for external gear For the calculation of h F, s Fn an α Fen, the proceure outline in the reference stanar ISO (Metho B) is to be use..3.4 Stress correction factor, Y S The stress correction factor Y 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. Y S applies to the loa application at the outer point of single tooth pair contact. Y S shall be etermine separately for the pinion an for the wheel. The stress correction factor, Y S, is to be etermine with the following equation (having range of valiity: 1 q 8 ): s Page 18 of 3 IACS Req. 1990/Rev.3 015

19 Where: Y q L S ( L) q s s sfn ρ F q s ρ F L notch parameter, root fillet raius in the critical section, mm s Fn /h F For h F an s Fn see clause 3.1 For the calculation of ρ F the proceure outline in the reference stanar ISO is to be use..3.5 Helix angle factor, Y β The helix angle factor, Y 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, Y β is to be calculate as follows: where: β Y β 1 ε β 10 β reference helix angle in egrees. The value 1.0 is substitute for ε β when ε β > 1.0, an 30 is substitute for β > Rim thickness factor, Y B The rim thickness factor, Y 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 Y B is to be etermine as follows: a) for external gears: if s R / h 1. Y B 1 if 0.5 < s R / h < 1. Y B 1.6 ln. 4 where: s R rim thickness of external gears, mm h tooth height, mm The case s R / h 0. 5 is to be avoie. h s R Page 19 of 3 IACS Req. 1990/Rev.3 015

20 b) for internal gears: if s / 3. 5 Y 1 R m n if 1.75 s / m < 3. 5 where: < R n B m Y B 1.15 ln s n R s R rim thickness of internal gears, mm The case s / is to be avoie. R m n.3.7 Deep tooth factor, Y DT The eep tooth factor, Y DT, ajusts the tooth root stress to take into account high precision gears an contact ratios within the range of virtual contact ratio.05 ε. 5, where: ε ε cos α αn β b αn Factor Y DT is to be etermine as follows: if ISO accuracy grae 4 an ε >. 5 Y 0. 7 αn if ISO accuracy grae 4 an.05 < αn. 5 YDT ε in all other cases Y 1. 0 DT ε αn DT.3.8 Bening enurance limit, σ FE For a given material, σ FE is the local tooth root stress which can be permanently enure. Accoring to the reference stanar ISO the number of 3x10 6 cycles is regare as the beginning of the enurance limit. σ FE is efine as the uniirectional pulsating stress with a minimum stress of zero (isregaring resiual stresses ue to heat treatment). Other conitions such as alternating stress or prestressing etc. are covere by the esign factor Y. The σ FE values are to correspon to a failure probability 1% or less. The enurance limit mainly epens on: - material composition, cleanliness an efects; - mechanical properties; - resiual stresses; - harening process, epth of harene zone, harness graient; - material structure (forge, rolle bar, cast). The bening enurance limit, σ FE is to be etermine, in general, making reference to values inicate in the reference stanar ISO , for material quality MQ..3.9 Design factor, Y The esign factor, Y, 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 σ FE. Page 0 of 3 IACS Req. 1990/Rev.3 015

21 The esign factor, Y, for loa reversing, is to be etermine as follows: Y 1.0 in general; Y 0.9 for gears with occasional part loa in reverse irection, such as main wheel in reversing gearboxes; Y 0.7 for iler gears.3.10 Life factor, Y N The life factor, Y 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 (Y δrelt,y RrelT, Y X). The life factor, Y N, is to be etermine accoring to Metho B outline in the reference stanar ISO Relative notch sensitivity factor, Y δrelt The relative notch sensitivity factor, Y 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. The relative notch sensitivity factor, Y δrelt, is to be etermine as follows: Y δrelt where: 1+ 0.ρ' ( 1+ q ) 1+ 1.ρ' s q s notch parameter (see clause 3.4) ρ slip-layer thickness, mm, from the following table Material ρ, mm case harene steels, flame or inuction harene steels N/mm² through-harene steels 1), yiel point R e 600 N/mm² N/mm² N/mm² nitrie steels ) The given values of ρ can be interpolate for values of R e not state above.3.1 Relative surface factor, Y RrelT The relative surface factor, Y 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. Page 1 of 3 IACS Req. 1990/Rev.3 015

22 The relative surface factor, Y RrelT is to be etermine as follows: R z < 1 1 R z 40 Material 1.10 case harene steels, through - harene steels ( R + 1) 0. 1 z ( σ B 800 N/mm ) normalise steels ( R + 1) z ( σ < 800 N/mm ) 1.05 ( ) R + 1 nitrie steels z B Where: R z mean peak-to-valley roughness of tooth root fillets, μm σ B tensile strength, N/mm The metho applie here is only vali when scratches or similar efects eeper than R z are not present. If the roughness state is an arithmetic mean roughness, i.e. R a value (CLA value) (AA value) the following approximate relationship can be applie: R CLA AA a R Size factor, Y X The size factor, Y X, takes into account the ecrease of the strength with increasing size. The factor mainly epens on: - material an heat treatment; - tooth an gear imensions; - ratio of case epth to tooth size. The size factor, Y X, is to be etermine as follows: Y X 1.00 for m n 5 generally Y X m n for 5 < m n < 30 Y X 0.85 for m n 30 Y X m n for 5 < m n < 5 Y X 0.80 for m n 5 normalise an through-harene steels surface harene steels.3.14 Safety factor for tooth root bening stress, S F The safety factor for tooth root bening stress, S F, can be assume by the Society taking into account the type of application. The following guiance values can be aopte: - Main propulsion gears: 1.55 to.00 - Auxiliary gears: 1.40 to 1.45 Page of 3 IACS Req. 1990/Rev.3 015

23 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 Society. En of Document Page 3 of 3 IACS Req. 1990/Rev.3 015