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

Transcription

1 (990) (Re. 994/ Corr. 996) (Re. Oct 03) Marine gears loa capacity of inolute parallel axis spur an helical gears. 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 efinitions apply to enclose gears, both intene for main propulsion an for essential auxiliary serices, which accumulate a large number of loa cycles (seeral millions), as require by the Rules of the Society. The following efinitions eal with the etermination of loa capacity of external an internal inolute spur an helical gears, haing parallel axis, with regar to surface urability (pitting) an tooth root bening strength an to this purpose the releant basic equations are proie in Parts an 3. The influence factors common to sai equations are escribe in the present Part. The others, introuce in connection with each basic equation, are escribe in the following Parts an 3. All influence factors are efine regaring their physical interpretation. Some of the influence factors are etermine by the gear geometry or hae been establishe by conentions. These factors are to be calculate in accorance with the equations proie. Other factors, which are approximations, can be calculate accoring to methos acceptable to the Society...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. Note: "The requirements of UR Re. are to be uniformly implemente from. January 05 by all IACS Societies to any Marine Gear subject to approal an to any Type Approe Marine gear from the ate of the first renewal after. January 05. For a Marine gear approe 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 UR Re. may be waie." Page of 5 IACS Req. 990/Re. 03

2 SI units hae been aopte. a centre istance mm b common face with mm b, face with of pinion, wheel mm 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 F t nominal tangential loa N F bt nominal tangential loa on base cyliner in the transerse section N h tooth epth mm m n normal moule mm m t transerse moule mm n, rotational spee of pinion, wheel res/min (rpm) P maximum continuous power transmitte by the gear set kw T, torque in way of pinion, wheel Nm u gear ratio linear spee elocity at pitch iameter m/s x, aenum moification coefficient of pinion, wheel z number of teeth z, number of teeth of pinion, wheel z n irtual number of teeth α n normal pressure angle at reference cyliner α t transerse pressure angle at ref. cyliner α tw transerse pressure angle at working pitch cyliner β helix angle at reference cyliner β b helix angle at base cyliner ε α transerse contact ratio ε β oerlap ratio total contact ratio ε γ Page of 5 IACS Req. 990/Re. 03

3 ..4 Geometrical efinitions For internal gearing z, a,, a, b an w are negatie. The pinion is efine as the gear with the smaller number of teeth, therefore the absolute alue of the gear ratio, efine as follows, is always greater or equal to the unity: uz /z w / w / For external gears u is positie, for internal gears u is negatie. 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 or b are the face withs at the respectie tooth roots. In any case, b 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 hae been aopte. tanα t tanα n cos β tan β tan β cos b α t zm n cos β, z, m n cos β b cos αt w cosαtw b,, t cosα w w a u + au u + where a 0.5 ( + ) w w z z n ( cos β cos β ) b z n, z, cos β cos β b mn m t cos β πα inα tanα ; α [ ] 80 in + x α tw inα t + tanα n or z + z x cosα tw m t ( z z ) + a cosα t ε α 0.5 a b πm ± 0.5 n a cosα cos β t b a sinα tw Page 3 of 5 IACS Req. 990/Re. 03

4 ε α 0,5 a b ± 0,5 π m t a cosα t b a sinα the positie sign is use for external gears, the negatie sign for internal gears b sin β ε β b sin β π( mm) ε β π for ouble helix, b is to be taken as the with of one helix ε ε + ε γ α β m n n 3,, 9099 π, n, / 60 0 tw..5 Nominal tangential loa, F t The nominal tangential loa, F t, tangential to the reference cyliner an perpenicular to the releant axial plane, is calculate irectly from the maximum continuous power transmitte by the gear set by means of the following equations: T 9549P n,, T, P π n, F t 000 T, /,..6 General influence factors..6. Application factor, A ) The application factor, A, accounts for ynamic oerloas from sources external to the gearing. A, for gears esigne for infinite life is efine as the ratio between the maximum repetitie 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 riing an rien machines; - ratio of masses; - type of couplings; - operating conitions (oerspees, changes in propeller loa conitions,...). When operating near a critical spee of the rie system, a careful analysis of conitions must be mae. The application factor, A, shoul be etermine by measurements or by system analysis acceptable to the Society. Where a alue etermine in such a way cannot be supplie, the following alues can be consiere. a) Main propulsion - iesel engine with hyraulic or electromagnetic slip coupling :.00 - iesel engine with high elasticity coupling :.30 - iesel engine with other couplings :.50 Page 4 of 5 IACS Req. 990/Re. 03

5 ) Where the essel, on which the reuction gear is being use, is receiing 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. b) Auxiliary gears - electric motor, iesel engine with hyraulic or electromagnetic slip coupling :.00 - iesel engine with high elasticity coupling :.0 - iesel engine with other couplings : Loa sharing factor, γ The loa sharing factor, γ accounts for the malistribution of loa in multiple path transmissions (ual tanem, epicyclic, ouble helix, etc.) γ is efine as the ratio between the maximum loa through an actual path an the eenly share loa. The factor mainly epens on accuracy an flexibility of the branches. The loa sharing factor, γ, shoul be etermine by measurements or by system analysis. Where a alue etermine in such a way cannot be supplie, the following alues can be consiere for epicyclic gears: - up to 3 planetary gears :.00-4 planetary gears :.0-5 planetary gears :.30-6 planetary gears an oer : Internal Dynamic factor, The internal ynamic factor,, accounts for internally generate ynamic loas ue to ibrations of pinion an wheel against each other. is efine as the ratio between the maximum loa which ynamically acts on the tooth flanks an the maximum externally applie loa (F t A γ ). The factor mainly epens on: - transmission errors (epening on pitch an profile errors); - masses of pinion an wheel; - gear mesh stiffness ariation as the gear teeth pass through the meshing cycle; - transmitte loa incluing application factor; - pitch line elocity; - ynamic unbalance of gears an shaft; - shaft an bearing stiffnesses; - amping characteristics of the gear system. The ynamic factor,, can is to be calculate as follows: TheThis metho may be applie only to cases where all the following conitions are satisfie: a) steel gears of heay rims sections b) F t b > 50N / mm Page 5 of 5 IACS Req. 990/Re. 03

6 c) z < 50 - ) running spee elocity in the subcritical range, i.e.: - for helical gears z 00 4 < - for spur gears z 00 0 z u 00 + u < 0 m/s < - spur gears ( 0 ) β an helical gears with β 30 - pinion with relatiely low number of teeth, z < 50 - soli isc wheels or heay steel gear rim This metho may be applie to all types of gears if z 00 3 as to helical gears where β > 30. < z u 00 + u < 3 m/s, as well For gears other than the aboe, reference can is to be mae to Metho B outline in the reference stanar ISO For helical gears of oerlap ratio > unity For spur gears is obtaine from Fig... is obtaine from Fig... For helical gears of oerlap ratio < unity is obtaine by means of linear interpolation between the alues obtaine from Fig.. an.: Where: ( ) ε β is the alue for helical gears, gien by Fig.. is the alue for spur gears, gien by Fig.. can also be etermine as follows: + z ( ) 00 alues are specifie in the following Table. a) For spur gears an for helical gears with oerlap ratio ε β z u F t 00 + u A b Page 6 of 5 IACS Req. 990/Re. 03

7 If A F t /b is less than 00 N/mm, this alue is assume to be equal to 00 N/mm. Numerical alues for the factor are to be as specifie in the Table. ISO accuracy graes ) spur gears helical gears ISO GRADES OF ACCURACY Spur gears Helical gears Table. Values of the factor for the calculation of 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: z u If 0. then u z u If > u z u then u b) For helical gears with oerlap ratio ε β < the alue is etermine by linear interpolation between alues etermine for spur gears ( α ) an helical gears ( β ) in accorance with: Where: ( ) α ε β α β α is the alue for spur gears, in accorance with a); β is the alue for helical gears, in accorance with a). ) ISO graes of accuracy accuracy graes accoring to ISO 38. In case of mating gears with ifferent graes of accuracy accuracy graes, the grae corresponing to the lower accuracy shoul be use. Page 7 of 5 IACS Req. 990/Re. 03

8 Fig.. Dynamic factor for helical gear. ISO graes of accuracy 3-8 z /00 (m/s) Fig.. Dynamic factor for spur gear. ISO graes of accuracy 3-8 Page 8 of 5 IACS Req. 990/Re. 03

9 ..6.4 Face loa istribution factors, Hβ an Fβ 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. Hβ is efine as follows: Hβ maximum loaper unit face with mean loa per unit face with Fβ is efine as follows: 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 resp. b. Fβ can be expresse as a function of the factor Hβ. 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.). The face loa istribution factors, Hβ for contact stress, an Fβ for tooth root bening stress, can are to be etermine accoring to the mmetho CC outline in the reference stanar ISO 6336/-stanar. Alternatie methos acceptable to the Society may be applie. a) In case the harest contact is at the en of the face with Fβ is gien by the following equations: N Fβ H β 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 alue 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): Fβ Hβ Page 9 of 5 IACS Req. 990/Re. 03

10 ..6.5 Transerse loa istribution factors, Hα an Fα The transerse 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 transersal loa istribution between two or more pairs of teeth in mesh. The factors Hα an Fα mainly epen on: - total mesh stiffness; - total tangential loa F t, A, γ,, Hβ ; - base pitch error; - tip relief; - running-in allowances. The transerse loa istribution factors, Hα for contact stress an Fα for tooth root bening stress, can are to be etermine accoring to mmetho B outline in the reference stanar ISO Surface urability (pitting).. 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... Contact stress σ H σ H0 A γ Hα Hβ σ HP where: σ H0 basic alue of contact stress for pinion an wheel ( u + ) Ft σ H 0 B H E ε β for pinion b u where: ( u + ) Ft σ H 0 D H E ε β for wheel b u B single pair mesh tooth contact factor for pinion (see clause.3) D single pair mesh tooth contact factor for wheel (see clause.3) H zone factor (see clause.4) E elasticity factor (see clause.5) Page 0 of 5 IACS Req. 990/Re. 03

11 ε contact ratio factor (see clause.6) β helix angle factor (see clause.7) F t b u nominal tangential loa at reference cyliner in the transerse section (see Part ) common face with reference iameter of pinion gear ratio (for external gears u is positie, for internal gears u is negatie) Regaring factors A, γ,, Hα an Hβ, see Part.... Permissible contact stress The permissible contact stress σ HP is to be ealuate separately for pinion an wheel: σ HP σ S H lim H N L 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.0) spee elocity factor (see clause.0) R roughness factor (see clause.0) W harness ratio factor (see clause.) X size factor for contact stress (see clause.) S H safety factor for contact stress (see clause.3)..3 Single pair mesh tooth contact factors, B an D The single pair mesh tooth contact factors, B for pinion an D for wheel, account for the influence on contact stresses of the tooth flank curature of the tooth flank curature 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 curature at the inner point of single pair contact. The single pair mesh tooth contact factors, B for pinions an D for wheels, can are to be etermine as follows: Page of 5 IACS Req. 990/Re. 03

12 For spur gears, ε β 0 B M or whicheer is the larger alue D M or whicheer is the larger alue M a b π z tanα tw a b ( ε ) α π z M a b π z tanα tw a b ( ε ) α π z For helical gears when ε β B D For helical gears when ε β < the alues of B an D are etermine by linear interpolation between B an D for spur gears an B an D for helical gears haing ε β. Thus: B D ( M ) an ( M ) an M ε β B M ε β D For internal gears, D shall be taken as equal to...4 one factor, H The zone factor, H, accounts for the influence on the Hertzian pressure of tooth flank curature at pitch point an relates transforms the tangential force loa at the reference cyliner to the normal force loa at the pitch cyliner. The zone factor, H, can is to be calculate as follows: Page of 5 IACS Req. 990/Re. 03

13 H cos β t b cos α tanα tw H cos β b cosα cos α sinα t tw tw..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 Hertz pressure contact stress. The elasticity factor, E, for steel gears (E N/mm, ν 0.3) is equal to: E 89.8 N/mm (N / mm) In other cases, reference can is to be mae to the reference stanar ISO Contact ratio factor, ε The contact ratio factor, ε, accounts for the influence of the transerse contact ratio an the oerlap ratio on the specific surface loa of gears. The contact ratio factor, ε, can is to be calculate as follows: Spur gears: ε 4 α ε 3 Helical gears: - for ε β < 4 ε 3 α ε ( ε ) β ε + ε β α - for ε β ε 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 ariables as the istribution of loa along the lines of contact. β is epenent only on the helix angle. The helix angle factor, β, can is to be calculate as follows: Page 3 of 5 IACS Req. 990/Re. 03

14 β cos β β cos β Where β is the reference helix angle...8 Enurance limit for contact stress, σ Hlim For a gien material, σ Hlim is the limit of repeate contact stress which can be permanently enure. The alue of σ Hlim can be regare as the leel of contact stress which the material will enure without pitting for at least 50 x 0 6 5x0 7 loa cycles. For this purpose, pitting is efine by: - for not surface harene gears: pitte area > % of total actie flank area - for surface harene gears: pitte area > 0,5% of total actie flank area, or > 4% of one particular tooth flank area. The σ Hlim alues are to correspon to a failure probability of % 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, can is to be etermine, in general, making reference to alues inicate in the stanar ISO 6336/-5, quality 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 harening heat treatment; - number of cycles; - influence factors ( R,, L, W, X ). The life factor, N, can is to be etermine accoring to mmetho B outline in the reference stanar ISO 6336/- stanar...0 Influence factors on of lubrication film on contact stress, L, an R The lubricant factor, L, accounts for the influence of the type of lubricant an its iscosity, the. The spee elocity factor,, accounts for the influence of the pitch line elocity an the roughness factor,. The roughness factor, R, accounts for the influence of the surface roughness on the surface enurance capacity. Page 4 of 5 IACS Req. 990/Re. 03

15 The factors may be etermine for the softer material where gear pairs are of ifferent harness. The factors mainly epen on: - iscosity of lubricant in the contact zone; - the sum of the instantaneous elocities of the tooth surfaces; - loa; - relatie raius of curature at the pitch point; - surface roughness of teeth flanks; - harness of pinion an gear. The lubricant factor, L, the spee elocity factor,, an the roughness factor R can are to be calculate as follows: a) Lubricant factor, L The factor, L, can is to be calculate from the following equation: L C L ( C ) 4 L ν 40 In the range 850 N/mm σ H lim 00 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 > 00 N/mm, take C L 0.9 Where: ν 40 nominal kinematic iscosity of the oil at 40 C, mm /s b) Spee Velocity factor, The spee elocity factor,, can is to be calculate from the following equations: C V + ( C ) V In the range 850 N/mm σ Hlim 00 N/mm, C V can is to be calculate as follows: C V C L Page 5 of 5 IACS Req. 990/Re. 03

16 c) Roughness factor, R The roughness factor, R, can is to be calculate from the following equations: Where: R 3 R z0 C R R z R + R z z The peak-to-alley roughness etermine for the pinion R z an for the wheel R z are mean alues for the peak-to-alley roughness R z measure on seeral tooth flanks (R z as efine in the reference stanar ISO 6336-). R z 0 R 3 0 ρ re relatie raius of curature: ρ re ρ ρ ρ + ρ Wherein: ρ, 0.5 b, tanα tw (also for internal gears, b negatie sign) If the roughness state is an arithmetic mean roughness, i.e. R a alue (CLA alue) (AA alue) the following approximate relationship can be applie: R CLA AA a R z 6 In the range 850 N/mm σ Hlim 00 N/mm, C R is to be calculate as follows: CR σ H lim If σ Hlim < 850 N/mm, take C R 0.50 If σ Hlim > 00 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: W apply to the soft gear only. The factor mainly epens on: Page 6 of 5 IACS Req. 990/Re. 03

17 - harness of the soft gear; - alloying elements of the soft gear; - tooth flank roughness of the harer gear. The harness ratio factor, W, can be calculate as follows: W HB a) Surface-harene pinion with through-harene wheel If HB< 30 If 30 HB 470 If HB >470 Where: W W W 3. R zh 0.5 HB R 3 R zh 0.5 zh 0.5 HB Brinell harness of the tooth flanks of the softer material gear of the pair R zh equialent roughness, μm R zh R z 0.33 ( 0 / ρre ) ( Rz / Rz ) ( ν /500) ρ re relatie raius of curature (see clause.0 c) For HB < 30, W. will be use. For HB > 470, W.0 will be use. 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 HB HB u If. HB /HB ( u ) W If HB /HB >.7 ( ) If gear ratio u>0 then the alue u0 is to be use. W Page 7 of 5 IACS Req. 990/Re. 03

18 In any case, if calculate W < then the alue W.0 is to be use... 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 equialent raius of curature. For through-harene gears an for surface-harene gears with aequate caseepth relatie to tooth size an raius of relatie curature X. When the caseepth is relatiely shallow then a smaller alue of X shoul be chosen...3 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 alues can be aopte: - Main propulsion gears:.0 to.40 - Auxiliary gears:.5 to.0 For gearing of uplicate inepenent propulsion or auxiliary machinery, uplicate beyon that require for class, a reuce alue can be assume at the iscretion of the Society..3 Tooth root bening strength.3. 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 haing 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 mmetho A of the reference stanar ISO Basic equations.3.. Tooth root bening stress for pinion an wheel Page 8 of 5 IACS Req. 990/Re. 03

19 where: σ σ F F Ft bm n Y Y Y Y Y F S β B DT A γ Fα Fβ σ ( Ft bmn ) YFYSY β Aγ F αfβ σ FP FP 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, A, γ,, Fα, Fβ (see Part ) b (see Part, clause.4) m n (see Part, clause.3).3.. Permissible tooth root bening stress for pinion an wheel σ FEYY σ FP S F N Y δrelt Y RrelT Y X where: σ FE Y Y N σ FP ( σ FEYYN SF ) Yσ reltyrreltyx bening enurance limit esign factor life factor Y σrelt Y δrelt relatie notch sensitie sensitiity factor Y RrelT relatie surface factor Y X size factor safety factor for tooth root bening stress S F.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 irtual spur gear with irtual number of teeth n. The tooth form factor, Y F, can 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 Page 9 of 5 IACS Req. 990/Re. 03

20 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. For the calculation of Dimensions of h F, s Fn an α Fen the proceure outline in the reference stanar can be use 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 conert 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, can is to be etermine with the following equation (haing range of aliity: q 8 ): Y.+.3 L S ( L) q s s Where: q 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. Page 0 of 5 IACS Req. 990/Re. 03

21 For the calculation of ρ F the proceure outline in the reference stanar ISO can is to be use..3.5 Helix angle factor, Y β The helix angle factor, Y β, conerts the stress calculate for a point loae cantileer beam representing the substitute gear tooth to the stress inuce by a loa along an oblique loa line into a cantileer plate which represents a helical gear tooth. The helix angle factor, Y β can is to be calculate as follows: where: β Y β ε β 0 β reference helix angle in egrees. One The alue (.0) is substitute for ε β when ε β >.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 comprehensie analysis. Factor Y B is to be etermine as follows: a) for external gears: if s R / h. Y if 0.5 < / h <. where: s R B Y B.6 ln. 4 s R rim thickness of external gears, mm h tooth height, mm The case s R / h 0. 5 is to be aoie. b) for internal gears: if s / 3. 5 Y R m n if.75 < / R n < 3. 5 m n Y B.5 ln sr where: s R rim thickness of internal gears, mm The case s /. 75 is to be aoie. R m n B h s R.3.7 Deep tooth factor, Y DT Page of 5 IACS Req. 990/Re. 03

22 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 irtual 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 if ISO accuracy grae 4 an αn < ε αn YDT ε αn in all other cases Y. 0 DT DT.3.68 Bening enurance limit, σ FE For a gien material, σ FE 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. 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 coere by the esign factor Y. The σ FE alues 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 zone, harness graient; - material structure (forge, rolle bar, cast). The bening enurance limit, σ FE can is to be etermine, in general, making reference to alues inicate in the reference stanar ISO 6336/-5, for material quality MQ Design factor, Y The esign factor, Y, takes into account the influence of loa reersing an shrinkfit prestressing on the tooth root strength, relatie to the tooth root strength with uniirectional loa as efine for σ FE. The esign factor, Y, for loa reersing, can is to be etermine as follows: Y.0 in general; Y 0.9 for gears with occasional part loa in reerse irection, such as main wheel in reersing gearboxes; Y 0.7 for iler gears.3.80 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. Page of 5 IACS Req. 990/Re. 03

23 The factor mainly epens on: - material an harening heat treatment; - number of loa cycles (serice life); - influence factors (Y δrelt,y RrelT, Y X ). The life factor, Y N, can is to be etermine accoring to mmetho B outline in the reference stanar ISO 6336/-3 stanar..3.9 Relatie notch sensitiity factor, Y δrelt The relatie notch sensitiity factor, Y δrelt, inicates the extent to which the theoretically concentrate stress lies aboe the fatigue enurance limit. The factor mainly epens on material an relatie stress graient. The relatie notch sensitiity factor, Y δrelt, can is to be etermine as follows: - for notch parameter alues (see clause 3.) inclue in the range.5< q s <4, it can be assume: Y δ relt.0 - for notch parameter outsie sai range Y δ relt can be calculate as outline in the reference stanar. Y δrelt + 0.ρ' ( + q ) +.ρ' s where: 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 0.08 through-harene steels ), yiel point R e 600 N/mm² N/mm² N/mm² nitrie steels ) The gien alues of ρ can be interpolate for alues of R e not state aboe.3.0 Relatie surface factor, Y RrelT The relatie 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 alley surface roughness. The relatie surface factor, Y RrelT can is to be etermine as follows: Page 3 of 5 IACS Req. 990/Re. 03

24 R < R 40 Material z z ( R z ) 0. ( R z ) 0. ( R z ) 0. 0 ( R z ) 0. 0 ( R z ) ( ) case harene steels, through - harene steels ( σ 800 N/mm ) B normalise steels ( σ < 800 N/mm ) R + nitrie steels z B Where: R z mean peak-to-alley roughness of tooth root fillets, μm σ B tensile strength, N/mm The metho applie here is only ali 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 alue (CLA alue) (AA alue) 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, can is to be etermine as follows: Y X.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.3.4 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. Page 4 of 5 IACS Req. 990/Re. 03

25 The following guiance alues can be aopte: - Main propulsion gears:.55 to.00 - Auxiliary gears:.40 to.45 For gearing of uplicate inepenent propulsion or auxiliary machinery, uplicate beyon that require for class, a reuce alue can be assume at the iscretion of the Society. En of Document Page 5 of 5 IACS Req. 990/Re. 03