CLASSIFICATION NOTES Marine Gears - Calculation of Load Capacity of Involute Parallel Axis Spur and Helical Gears

Transcription

1 CLASSIFICATION NOTES CLASSIFICATION NOTES Marine Gears - Calculation of Load Capacity of Involute Parallel Axis Spur and Helical Gears January 2016 ASIA PACIFIC CLASSIFICATION SOCIETY P/1

2 CLASSIFICATION NOTES Contents Section 1 Basic Principles - Introduction and General Influence Factors 2 Surface Durability (Pitting) 3 Tooth Root Bending Strength

3 ASIA PACIFIC CLASSIFICATION SOCIETY P/1 Marine Gears - Calculation of Load Capacity of Involute Parallel Axis Spur and Helical Gears 1.1 Introduction Section 1 Basic Principles - Introduction and General Influence Factors The following requirements are mainly based on the ISO 6336 standard (hereinafter also called "reference standard ') for the calculation of load capacity of spur and helical gears. 1.2 Scope and field of application The following requirements apply to enclosed gears, both intended for main propulsion and for essential auxiliary services which accumulate a large number of load cycles (several millions), as required by the Rules These requirements deal with the determination of load capacity of external and internal involute spur and helical gears, having parallel axis, with regards to surface durability (pitting) and tooth root bending strength and to this purpose the relevant basic equations are provided in Sec.2 and The influence factors common to the equations in Sec.2 and 3 are described in this Section All influence factors are defined regarding their physical interpretation. Some of the influence factors are determined by the gear geometry or have been established by conventions. These 'factors are to be calculated in accordance with the equations provided. Other factors, which are approximations, may be calculated according to methods acceptable to the Committee. 1.3 Symbols and units The main symbols used are listed below. a... center distance, [mm] b common face width, [mm] b face width of pinion, wheel, [mm] d... reference diameter, [mm] d1,2... reference diameter of pinion, wheel, [mm] da tip diameter of pinion, wheel, [mm] dbl,2... base diameter of pinion, wheel, [mm] dfl.2... root diameter of pinion, wheel, [mm] dw1,2... working diameter of pinion, wheel, [mm] Ft... nominal tangential load, [N] Fbt... nominal tangential load on base cylinder in the transverse section, [N] h... tooth depth, [mm] mn... normal module, [mm] mt transverse module, [mmj nl.2... rotational speed of pinion, wheel, [revs/min]

4 P maximum continuous power transmitted by the gear set. [kw] T torque in way of pinion, wheel. [Nm] u... gear ratio, (-] v... linear speed at pitch diameter, [m/s] * addendum modification coefficient of pinion, wheel, [-] z number of teeth, [-] z number of teeth of pinion, wheel, [-] 2n... virtual number of teeth. [-] <«n... normal pressure angle at reference cylinder, f 0 ] «t transverse pressure angle at reference cylinder, [ ] "tw... transverse pressure angle at working pitch cylinder, [ J ft... helix angle at reference cylinder, [ ] ftb... helix angle at base cylinder, [ ]... transverse contact ratio. [-] eft... overlap ratio. [-J cy... total contact ratio, [-] 1.4 Geometrical definitions For internal gearing z2, a. d2, da2 and dw2 are negative The pinion is defined as the gear with the smaller number of teeth, therefore the absolute value of the gear ratio, defined as follows, is always greater or equal to the unity: u = Z2 Z1 dw2 = d2 dw1 dl For external gears u is positive, for internal gears u is negative In the equation of surface durability b is the common face width on the pitch diameter In the equation of tooth root bending stress b1 or b2 are the face widths at the respective tooth roots. In any case, b1 and b2 are not to be taken as greater than b by more than one module (mn) on either side The common face width b may be used also in the equation of teeth root bending stress if significant crowning or end relief have been adopted Following geometric proportions are to be used:,. tan an tan at = cos ft tan fib = tan ficos at, mn d = z cosft

5 db = dcosat mt cos fi = dwcosatw a = 0.5 [dw 1 + dw2) zn ^ {cosjibcosfi) m n invatw = invat + 2tgan-~] + ^21 y (z 1 +z2) _ 0 5 ^dat 2 - db 1 2 ± 05V da2 2 - c/b2 2 ~ a sinctfwnmn cos at/cosfi the positive sign is used for external gears, the negative sign for internal gears for double helix, b is to be taken as the width of one helix ey = e«+ e/3 c/1,2nt, Nominal tangential load, Ft The nominal tangential load, Ft, tangential to the reference cylinder and perpendicular to the relevant axial plane, is calculated directly from the maximum continuous power transmitted by the gear set by means of the following equations: Ft = ~1.2 cm General influence factors Application factor, KA a) The application factor, accounts for dynamic overloads from sources external to the gearing. b) Where the vessel, on which reduction gearing is used, is receiving an Ice Class notation, the Application Factor or the Nominal Tangential Force is to be adjusted to reflect the ice load associated with the contemplated Ice Class notation. c) KA, for gears designed for infinite life is defined as the ratio between the maximum repetitive cyclic torque applied to the gear set and the nominal rated torque. calculations. d) The nominal rated torque is defined by the rated power and speed and is the torque used in the rating

6 e) The factor mainly depends on: characteristics of driving and driven machines; - ratio of masses; - type of couplings; - operating conditions (overspeeds, changes in propeller load conditions, etc.) When operating near critical speed of the drive system, a careful analysis of conditions must be made. f) The application factor, KA, is to be determined by measurements or by system analysis acceptable to the Committee. Where a value determined in such a way cannot be supplied, the following values can be considered: i) Main propulsion diesel engine with hydraulic or electromagnetic slip coupling 1.00 diesel engine with high elasticity coupling 1.30 diesel engine with other couplings 1.50 ii) Auxiliary gears electric motor, diesel engine with hydraulic or electromagnetic slip coupling 1.00 diesel engine with high elasticity coupling 1.20 diesel engine with other couplings Load sharing factor, K v a) The load sharing factor, K, accounts for the maldistribution of load In multiple path transmissions (dual tandem, epicyclic, double helix, etc.). b) K y is defined as the ratio between the maximum load through an actual path and the evenly shared load. The factor mainly depends on accuracy and flexibility of the branches. c) The load sharing factor, K y, is to be determined by measurements or by system analysis. Where a value determined in such a way cannot be supplied, the following values can be considered for epicyclical gears: up to 3 planetary gears planetary gears planetary gears planetary gears and over Dynamic factor, Kv a) The dynamic factor, Kv, accounts for internally generated dynamic loads due to vibrations of pinion and wheel against each other. b) Kv is defined as the ratio between the maximum load which dynamically acts on the tooth flanks and the maximum externally applied load (Ft.KA. Ky). c) The factor mainly depends on: transmission errors (depending on pitch and profile errors):

7 - masses of pinion and wheel: gear mesh stiffness variation as the gear teeth pass through the meshing cycle; transmitted load including application factor; pitch line velocity; dynamic unbalance of gears and shaft; - shaft and bearing stiffness s: damping characteristics of the gear system. d) The method of calculation of dynamic factor, Kv. given herein may be applied only to cases where all the following conditions are satisfied: i) steel gears of heavy rims sections ii) Ft/b > 150 [N/mm] iii) zl < 50 «v) running speed in the subcritical range: for helical gears (vz1)/100 < 14 for spur gears (v z1)/100 < 10. This method may be applied to all types of gears if (v z1)/100 < 3 e) For gears other than the above, reference can be made to method B outlined in the reference standard. f) For helical gears of overlap ratio > unity Kv is obtained from Fig For spur gears Kv is obtained from Fig For helical gears of overlap ratio < unity Kv js obtained by means of linear interpolation between the values obtained from Fig and where, Kv = Kv2 - e/i (Kv2 - Kv1) Kv1 is the Kv value for helical gears, given by Fig Kv2 is the Kv value for spur gears, given by Fig g) Kv can also be determined as follows: Kv = K1 values are specified in the Table 1.6.1

8 Fig : Dynamic factor for helical gear Y - Zj/lOO(ni/s) » Fig : Dynamic factor for spur gear

9 Table 1.6.1: Values of the factor K1 for the calculation of Kv Note ISO grades of accuracy according to ISO In case of mating gears with different grades of accuracy the grade corresponding to the lower accuracy should be used Face load distribution factors KH/? and KF/? a) The face load distribution factors, KH/? for contact stress. KF/? for tooth root bending stress, account for the effects of non-uniform distribution of load across the face width. b) KH/? is defined as follows: tsujj _ maximum load per unit face width mean load per unit face width c) KF/? is defined as follows: _ maximum bending stress at tooth root per unit face width mean bending stress at tooth root per unit face width d) The mean bending stress at tooth root relates to the considered face width b1, b2 respectively. KF (i can be expressed as a function of the factor KH/i e) The factors KH/? and KF/? mainly depend on: gear tooth manufacturing accuracy; errors in mounting due to bore errors; - bearing clearances; wheel and pinion shaft alignment errors; elastic deflections of gear elements, shafts, bearings housing and foundations which support the gear elements; thermal expansion and distortion due to operating temperature; - compensating design elements (tooth crowning, end relief, etc.). f) The face load distribution factors. KH/? for contact stress, and KF/? for tooth root bending stress, can be determined according to the method C2 outlined in the ISO 6336/1 standard. Alternative methods acceptable to the Committee may be applied. i) In case the hardest contact is at the end of the face width KF/? is given by the following equations; KF/? = KH/? N K1 ISO Grades of Accuracy (See Note) Spur gears Helical gears N = p/h) 2 i+(b/h) + (b/hf

10 (b/h) = face width/tooth height ratio, the minimum of bl/h1 or b2/h2. For double helical gears, the face width of only one helix is to be used. ii) In case of gears where the ends of the face width are lightly loaded or unloaded (end relief or crowning): KFfi = KH/j Transverse load distribution factors, KH«and KF«a) The transverse load distribution factors KH«for contact stress and KFa for tooth root bending stress, account for the effects of pitch and profile errors on the transversal load distribution between two or more pairs of teeth in mesh. b) The factors KH«and KFa mainly depend on: - total mesh stiffness; - total tangential load, Ft, KA, Ky, Kv, KH/i; - base pitch error; - tip relief; running-in allowances. c) The transverse load distribution factors. KHa for contact stress and KF (i for tooth root bending stress, can be determined according to method B outlined in the reference standard.

11 Section 2 Surface Durability (Pitting) 2.1 Scope and general remarks The criterion for surface durability is based on the Hertz pressure on the operating pitch point or at the inner point of single pair contact. The contact stress oh must be equal to or less than the permissible contact stress CTHP. 2.2 Basic equations Contact stress where, oh = oho 'J KAKy KvKHa KH/3 ohp oho = basic value of contact stress for pinion and wheel where, ZB = single pair mesh factor for pinion, see 2.3 ZD = single pair mesh factor for wheel, see 2.3 ZH = zone factor, see 2.4 ZE = elasticity factor, see 2.5 Ze = contact ratio factor, see 2.6 Z (i = helix angle factor, see 2.7 Ft = nominal tangential load at reference cylinder in the transverse section, See Sec.1 (for external gears u is positive, for internal gears u is negative) b = common face width d1 = reference diameter of pinion u = gear ratio Regarding factors KA, Ky, Kv, KHa and KHfi, See Sec Permissible contact stress The permissible contact stress crhp is to be evaluated separately for pinion and wheel as under:

12 where, ohp = uhlinmzlzvzrzwzx on ohiim = endurance limit for contact stress, see 2.8 ZN - life factor for contact stress, see 2.9 ZL - lubrication factor, see 2.10 Zv = speed factor, see 2.10 ZR = roughness factor, see 2.10 ZW = hardness ratio factor, see 2.11 ZX - size factor for contact stress, see 2 12 SH = safety factor for contact stress, see Single pair mesh factors. ZB and ZD The single pair mesh factors. ZB for pinion and ZD for wheel, account for the influence on contact stresses of the tooth flank curvature at the inner point of single pair contact in relation to ZH The factors transform the contact stresses determined at the pitch point to contact stresses considering the flank curvature at the inner point of single pair contact The single pair mesh factors, ZB for pinions and ZD for wheels, can be determined-g,s follows: For spur gears, e/i = 0. ZB - M1 or 1 whichever is the larger value ZD = M2 or 1 whichever is the larger value Ml = tgnarw («T - 1) V ( dal \ dbl) da2]2 db2 For helical gears when c (i 1 ZB = ZD = For helical gears when q8 < 1 the values of ZB, ZD are determined by linear interpolation between ZB, ZD for spur gears and ZB, ZD for helical gears having rji 1. Thus: ZB = M1 - f />' (M1-1) and ZB > 1 ZD = M2 - eft (M2-1) and ZD > 1

13 2.4 Zone factor. ZH The zone factor. ZH. accounts for the influence on the Hertzian pressure of tooth flank curvature at pitch point and relates the tangential force at the reference cylinder to the normal force at the pitch cylinder The zone factor, ZH, can be calculated as follows: _ -y/ pcos/fo cos ZH cos nt sin utw 2.5 Elasticity factor, ZE The elasticity factor. ZE. accounts for the influence of the material properties E (modulus of elasticity) and r (Poisson's ratio) on the Hertz pressure The elasticity factor. ZE. tor steel gears (E = (N/mm 2 ]. t- = 0 3) is equal to: ZE (N,/2 /mm) In other cases, reference can be made to the reference standard. 2.6 Contact ratio factor. Z< The contact ratio factor Z< accounts for the influence of the transverse contact ratio and the overlap ratio on the specific surface load of gears The contact ratio factor. Zr. can be calculated as follows Spur gears: ZF- V^ Helical gears: for efi < 1 for efi > 1 Zr = V- 4 ' (1 -r/f) +ejt v ' r«2.7 Helix angle lactor, Zf> The helix angle factor, ZJI, accounts for the influence of helix angle on surface durability, allowing for such variables as the distribution of load along the lines of contact Z/f is dependent only on the helix angle The helix angle factor, Zji. can be calculated as follows: Z/f = v COSft where />' is the reference helix angle.

14 2.8 Endurance limit for contact stress, ahlim For a given material. ahlim is the limit of repeated contact stress which can be permanently endured. The value of ohkm can be regarded as the level of contact stress which the material will endure without pitting for at least load cycles For this purpose, pitting is defined by: for non-surface hardened gears for surface hardened gears pitted area > 2 per cent of total active flank area pitted area > 0.5 per cent of total active flank area, or > 4 per cent of one particular tooth flank area The ahlim values are to correspond to a failure probability of 1 per cent or less The endurance limit mainly depends on: - material composition, cleanliness and defects. - mechanical properties; - residual stresses; hardening process, depth of hardened zone, hardness gradient; - material structure (forged, rolled bar, cast) The endurance limit for contact stress ahlim, can be determined, in general, making reference to values indicated in ISO 6336/5, quality MQ. 2.9 Life factor, ZN The life factor. ZN. accounts for the higher permissible contact stress in case a limited life (number of cycles) is required The factor mainly depends on: - material and hardening; - number of cycles; - influence factors (ZR. Zv, ZL. ZW, ZX) The life factor, ZN, can be determined according to method outlined in the ISO 6336/2 standard Influence factors on lubrication film, ZL, Zv and ZR The lubricant factor. ZL, accounts for the influence of the type of lubricant and its viscosity, the speed factor, Zv, accounts for the influence of the pitch line velocity and the roughness factor, ZR. accounts for the influence of the surface roughness on the surface endurance capacity The factors are to be determined for the softer material where gear pairs are of different hardness The factors mainly depend on: viscosity of lubricant in the contact zone; - the sum of the instantaneous velocities of the tooth surfaces; - load;

15 - relative radius of curvature at the pitch point; surface roughnesses of teeth flanks; - hardness of pinion and gear The lubricant factor, ZL, the speed factor, ZV, and the roughness factor ZR can be calculated as follows: a) Lubricant factor. ZL The factor, ZL, can be calculated from the following equation: ZL = CZL + 4(1.0 - CZL) ( /i< 40) 2 In the CZL = range [N/mm 2 ] < ohiim < 1200 [N/mm 2 ], CZL can be calculated as follows: I ohiim If ohiim < 850 [N/mm 2 ], take CZL = 0.83 If ohiim > 1200 [N/mm 2 ], take CZL = 0.91 where, p t 40 = nominal kinematic viscosity of the oil at 40 C, [mm Is] b) Speed factor, Zv The speed factor, Zv. can be calculated from the following equations: In the range 850 I ohiim [N/mm 2 ] { 350 < ohiim < 1200 [N/mm 2 ], CZv can be calculated as follows: CZv = If ohiim < 850 [N/mm 2 ], take CZv = 0.85 If ohiim > 1200 [N/mm 2 ], take CZv = 0.93 c) Roughness factor, ZR The roughness factor, ZR. can be calculated from the following equations: where,

16 R zi + R z2 RZ ~ 2 The peak-to-valley roughness determined for the pinion R Z1 and for the wheel R Z2 are mean values for the peak-to-valley roughness R2 measured on several tooth flanks (R2 as defined in the reference standard).

17 Relative radius of curvature: P1 P2 pred = - ' pi + P2 wherein: pi.2 = 0.5. dtn,2 tanafw (also for internal gears, db negative sign) If the roughness stated is an Ra value (= CLA value) (= AA value) the following approximate relationship can be applied: Ra = CLA = AA = Rz/6 In the range 850 [N/mm 2 ] uhlim 1200 [N/mm 2 ], CZR can be calculated as follows: CZR = rrhiim IfaHlim < 850 [N/mm 2 ], take CZR IfaHlim > 1200 [N/mm 2 ], take CZR = Hardness ratio factor, ZW The hardness ratio factor, ZW, accounts for the increase of surface durability of a soft steel gear meshing with a significantly harder gear with a smooth surface The factor ZW applies to the soft gear only and mainly depends on: hardness of the soft gear; - alloying elements of the soft gear; - tooth flank roughness of the harder gear. ZW= 1.2 HB The hardness ratio factor. ZW, can be calculated as follows: where, HB Brinell hardness of the softer material For HB. < 130. ZW = 1.2 is to be used. For HB > 470, ZW = 1.0 is to be used Size factor. ZX The size factor, ZX, accounts for the influence of tooth dimensions on permissible contact stress and reflects the non-uniformity of material properties The factor mainly depends on: material and heat treatment;

18

19 - tooth and gear dimensions; - ratio of case depth to tooth size. - ratio of case depth to equivalent radius of curvature For through-hardened gears and for surface-hardened gears with adequate case depth relative to tooth size and radius of relative curvature, Z* = 1. When the case depth is relatively shallow then a smaller value of Zx should be chosen Safety factor for contact stress, SH The safety factor for contact stress, SH, would be assumed by the Committee taking into account the type of application based upon the following guidance: r Main propulsion gears Auxiliary gears For gearing of duplicated independent propulsion or auxiliary machinery, duplicated beyond that required for class, a reduced value may be assumed at the discretion of the Committee.

20 Section 3 Tooth Root Bending Strength 3.1 Scope and general remarks The criterion for tooth root bending strength is the permissible limit of local tensile strength in the root fillet The root stress of and the permissible root stress a FP are to be calculated separately for the pinion and the wheel c/f must not exceed ofp The following requirements apply to gears having rim thickness greater than 3.5 mn. 3.2 Basic equations Tooth root bending stress for pinion and wheel F = YF YS Yp KA Ky Kv KFa KF/i ofp where, YF = tooth form factor, see 3.3 YS = stress correction factor, see 3.4 Yji = helix angle factor, see 3.5 For definitions of b. Ft. KA. Ky, Kv, KF«. KF/j see Sec Permissible tooth root bending stress for pinion and wheel ufp = Y d r e l T YRrelT YX where, afe = bending endurance limit, see 3.6 Yd = design factor, see 3.7 YN = life factor, see 3.8 YdrelT = relative notch sensitivity factor, see 3.9 YRrelT = relative surface factor, see 3.10 YX = size factor, see 3.11 SF = safety factor for tooth root bending stress, see 3.12

21 3.3 Tooth form factor. YF 3,3.1 The tooth form factor. YF, represents the influence on nominal bending stress of the tooth form with load applied at the outer point of single pair tooth contact. YF is to be determined separately for the pinion and the wheel. In the case of helical gears, the form factors for gearing are to be determined in the normal section, i.e. for the virtual spur gear with virtual number of teeth zn The tooth form factor, YF, can be calculated as follows: mn YF = 6 cosafen 2 cosan where. hf bending moment arm for tooth root bending stress for application of load at the outer point of single tooth pair contact, [mm] sfn tooth root chord in the critical section, [mm] «Fen = pressure angle at the outer point of single tooth pair contact in the normal section, [ ] The result of rating calculations made by following this method are acceptable for normal pressure angles up to 25 and reference helix angles up to 30. For larger pressure angles and larger helix angles, the calculated results should be confirmed by experience as by method A of the reference standard. 3.4 Stress correction factor, YS The stress correction factor. YS. is used to convert the nominal bending stress to the local tooth root stress, taking into account that not only bending stresses arise at the root YS applies to the load application at the outer point of single tooth pair contact and is to be determined separately for the pinion and for the wheel and can be determined with the following equation (having range of validity: 1 qs < 8): where, i YS = ( L) qs 1-21+;!51 qs sfn 2,>F qs - notch parameter pf= root fillet radius in the critical section, [mm]

22 JL 120 See Fig for hf and sfn. For the calculation of hf the procedure outlined in the reference standard can be used. 3.5 Helix angle factor, Yfi The helix angle factor. Y/f. converts the stress calculated for a point loaded cantilever beam representing the substitute gear tooth to the stress induced by a load along an oblique load line into a cantilever plate which represents a helical gear tooth The helix angle factor, Yji, can be calculated as follows: where. Y/i = 1 - rfi ji = reference helix angle in degrees. One (1 0) is substituted for eji when eft > 1.0. and 30 is substituted for when ji > Bending endurance limit, crfe For a given material, crfe is the local tooth root stress which can be permanently endured and the number of cycles is to be regarded as the beginning of the endurance limit (JFE is defined as the unidirectional pulsating stress with a minimum stress of zero (disregarding residual stresses due to heat treatment). Other conditions such as alternating stress or prestressing etc. are covered by the design factor Yd The «FE values are to correspond to a failure probability of 1 per cent or less The endurance limit mainly depends on: - material composition, cleanliness and defects;

23 - mechanical properties: - residual stresses; hardening process, depth of hardened zone, hardness gradient; material structure (forged, rolled bar. cast) The bending endurance limit, CTFE, can be determined, generally in accordance the values indicated in ISO 6336/5. quality MQ. 3.7 Design factor, Yd The design factor, Yd, takes into account the influence of load reversing and shrinkfit prestressing on the tooth root strength, relative to the tooth root strength with unidirectional load as defined for afe The design factor, Yd, for load reversing, can be determined as follows: Yd = 1.00 in general; 3.8 Life factor, YN 0.9 for gears with occasional part load in reversed direction, such as main wheel in reversing gearboxes; 0.7 for idler gears The life factor, YN, accounts for the higher tooth root bending stress permissible in case a limited life (number of cycles) is required. The factor mainly depends on:. - material and hardening: - number of cycles; - influences factors (YdrelT, YRrelT, YX) The life factor, YN. can be determined according to method B outlined in ISO 6336/3 standard. 3.9 Relative notch sensitivity factor, YdrelT The relative notch sensitivity factor, YdrelT. indicates the extent to which the theoretically concentrated stress lies above the fatigue endurance limit The relative notch sensitivity factor, YdrelT, mainly depends on material and relative stress gradient and can be determined as follows: for notch parameter values (see 3.2) included in the YRrelT = 1.0 range 1 5 < qs < 4 for notch parameter outside the above range YRrelT can be calculated as outlined in the reference standard Relative surface factor. YRrelT The relative surface factor, YRrelT, takes into account the dependence of the root strength on the surface condition in the tooth root fillet, mainly the dependence on the peak to valley surface roughness The relative surface factor, YRrelT. can be determined as follows:

24 Rz < 1 1 < Rz < (Rz + 1) 01 case hardened steels through - hardened steels (ab 800 [N/mm 2 ]) (Rz + 1) 0 01 normalized steels (ab < 800 [N/mm 2 ]) (Rz 1 1) nitrided steels where. Rz =- mean peak to-valley roughness of tooth root fillets. [/<m] CTB - tensile strength in [N/mm 2 ] The method applied here is only valid when scratches or similar defects deeper than 2 Rz are not present If the roughness staled is an Ra value (= CLA value) (= AA value) the following approximate relationship can be applied: Ra = CLA = AA Rz/ Size factor, YX The size factor. YX. takes into account the decrease of the strength with increasing size The factor mainly depends on: material and heat treatment: - tooth and gear dimensions; ratio of case depth to tooth size The size factor, YX. can be determined as follows: YX for mn < 5 generally,! YX mn for 5 < mn < 30 normalized and through hardened ; YX = 0.85 for mn > 30 steels I YX = mn for 5 < mn < 25 surface hardened steels YX = 0 80 for mn > Safety factor for tooth root bending stress. SF The safety factor for tooth root bending stress, SF. may be assumed by the Committee taking into account the type of application The following guidance values may be adopted: Main propulsion gears Auxiliary gears For gearing of duplicated independent propulsion or auxiliary machinery, duplicated beyond that required for class, a reduced value may be assumed at the discretion of the Committee.