Section 4 Design of gearing

4.1.1 For the purposes of this Chapter the following symbols apply:

Subscript:

4.2.1 The tooth profile in the transverse section is to be of involute shape, and the roots of the teeth are to be formed with smooth fillets of radii not less than 0,25 m _n.

4.2.2 All sharp edges left on the tips and ends of pinion and wheel teeth after hobbing and finishing are to be removed.

4.3.1 For values of application factor, K _A, see Table 1.4.1 Values of K _A .

4.3.2 Load sharing factor, K _γ. When a gear drives two or more mating gears where the total transmitted load is not evenly distributed between the individual meshes, a factor, K _γ, is to be applied. K _γ is defined as the ratio between the maximum load through an actual path and the evenly shared load. This is to be determined by measurements. Where a value cannot be determined in such a way, the values in Table 1.4.2 Values of K _y may be considered:

4.3.3  Dynamic factor, K _V, is to be calculated as follows when all the following conditions are satisfied:

• spur gears (β = 0°) and helical gears with β ≤ 30°
• pinion with relatively low number of teeth, z₁ < 50
• solid disc wheels or heavy steel gear rim

Or this method may also be applied to all types of gears if:

And to helical gears where β > 30°

1. For spur gears and for helical gears with ∊_β ≥ 1:

   

   Where K _A F _t/b is less than 100 N/mm, the value 100 N/mm is to be used. Numerical values for the factor K ₁ are to be as specified in the Table 1.4.3 Values of K ₁

1. For all accuracy grades the factor K ₂ is to be in accordance with the following:

   • for spur gears K ₂ = 0,0193
   • for helical gears K ₂ = 0,0087

   Factor K ₃ is to be in accordance with the following:

   
   

2. For helical gears with overlap ratio ∊_β < 1, the value K _v is to be determined by linear interpolation between values determined for spur gears (K _vα) and helical gears (K _vβ) in accordance with:

   

   K _vα is the K _v value for spur gears, in accordance with Pt 11, Ch 1, 4.3 Tooth loading factors 4.3.3

   K _vβ is the K _v value for helical gears, in accordance with Pt 11, Ch 1, 4.3 Tooth loading factors 4.3.4.(b)

4.3.5  Longitudinal load distribution factors, K _Hβ and K _Fβ:

Calculated values of K _Hβ > 2 are to be reduced by improved accuracy and helix correction as necessary:

The following minimum values are applicable, these also being the values where helix correction has been applied:

For through-hardened steels and surface hardened steels running on through-hardened steels:

For surface hardened steels, when

4.3.6  Transverse load distribution factors, K _{H α} and K _{F α}

1. Values K _Hα and K _Fα for gears with total contact ratio ∊_γ ≤ 2

   

2. Values K _Hα and K _Fα for gears with total contact ratio ∊_γ > 2

   

   Limiting conditions for K_Hα:

   If when calculated in accordance with (a) or (b), then

   If K _Hα< 1 when calculated in accordance with (a) or (b), then K _Hα =1

   Limiting conditions for K _Fα:

   If when calculated in accordance with (a) or (b), then

   If K _Fα< 1 when calculated in accordance with (a) or (b), then K _Fα=1

When tip relief is applied f _pb is to be half of the maximum specified value:

y _α ≤ 3 μm

When pinion and wheel are manufactured from different materials:

4.3.7  Tooth mesh stiffness, C _γ:

For internal gears Z _n2 = ∞

Other calculation methods for C _γ will be specially considered.

4.4.1 The Hertzian contact stress, σ_H, at the pitch circle is not to exceed the allowable Hertzian contact stress, σ_HP.

and

for the pinion/wheel combination

where

Z _∊, contact ratio factor is to be calculated as follows:

for helical gears:

for spur gears

where:

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 R _z measured on several tooth flanks.

relative radius of curvature:

where:

For internal gears, d _b has a negative sign.

If R _a, the surface roughness of the tooth flanks is given then the following approximation may be applied:

C _ZR is to be taken from Table 1.4.4 Values of C _ZR .

For values of Z _x, see Table 1.4.5 Values of Z_x

σ_{H lim,} see Table 1.4.6 Values of endurance limit for Hertzian contact stress, σ _{H lim}

S _{H min,} see Table 1.4.7 Factors of safety

4.5.1 The bending stress at the tooth root, σ_F is not to exceed the allowable tooth root bending stress σ_FP:

For values of S _{F min}, see Table 1.4.7 Factors of safety

Stress correction factor Y _ST = 2.

4.5.2  Tooth form factor, Y _F:

where h _F, α_Fen and S _Fn are shown in Figure 1.4.1 Normal tooth section.

E, h _ao, α_n, S _pr and ρ_ao are shown in Figure 1.4.2 External tooth forms.

4.5.3 For internal tooth forms the form factor is calculated, as an approximation, for a substitute gear rack with the form of the basic rack in the normal section, but having the same tooth depth as the internal gear:

where α_{F en} is taken as being equal to α_n

d _en2 is calculated as d _en for external gears, and

4.5.4  Stress concentration factor, Y _s

when q _s < 1 the value of Y _s is to be specially considered.

The formula for Y _s is applicable to external gears with α_n = 20^o but may be used as an approximation for other pressure angles and internal gears.

4.5.5  Helix angle factor Y _β

but

Y _b ≥ 1 − 0,25 _β ≥ 0,75

4.5.6  Rim thickness factor, Y _B

Factor Y _B is to be determined as follows:

1. For external gears

   If S _R/h ≥ 1,2 then Y _B = 1

   If 0,5 < S _R/h <1,2 then

   where

   S R

   =

   rim thickness of external gears, mm

   The case S _R/h ≤ 0,5 is to be avoided.

2. For internal gears

   If S _R/m_n ≥ 3,5 then Y _B = 1

   If 1,75 < S _R/m_n < 3,5 then

   Where
   S _R = rim thickness of internal gears, mm

   The case S _R/m_n ≤ 1,75 is to be avoided.

4.5.7  Deep tooth factor Y _DT

The deep tooth factor, Y _DT, adjusts the root stress to take into account high precision gears and contact ratios within the range of virtual contact ratio 2,05 ≤ ∊_αn ≤ 2,5 where:

Factor Y _DT is to be determined from Table 1.4.9 Values of deep tooth factor, Y _DT :

4.5.8  Relative notch sensitivity factor, Y_{δ rel T}

ρ’ = slip-layer thickness is to be taken from Table 1.4.10 Slip-layer thickness, ρ’

4.5.9  Relative surface finish factor, Y _{R rel T}

4.5.10  Size factor, Y _x

4.5.11  Design factor, Y _D

4.6.1 Factors of safety are shown in Table 1.4.7 Factors of safety.

4.7.1 The following symbols apply:

P in kW and R in rpm, see Pt 11, Ch 1, 1.2 Power ratings 1.2.1.

4.7.2 This sub-Section is applicable to the main and ancillary transmission shafting, enclosed within the gearcase.

4.7.3 The diameter of the enclosed gear shafting adjacent to the pinion or wheel is to be not less than the greater of d _b or d _t, where:

4.7.4 For the purposes of the above it is assumed that the pinion or wheel is mounted symmetrically spaced between bearings.

4.7.5 Outside a length equal to the required diameter at the pinion or wheel, the diameter may be reduced, if applicable, to that required for d _t.

4.7.6 For bevel gear shafts, where a bearing is located adjacent to the gear section, the diameter of the shaft is to be not less than d _t. Where a bearing is not located adjacent to the gear the diameter of the shaft will be specially considered.

4.7.7 The diameter of quill shaft (not axially constrained and subject only to external torsional loading) is to be not less than given by the following formula:

Diameter of quill shaft =

4.7.8 Where a shaft, located within the gearcase, is subject to the main propulsion thrust, the diameter at the collars of the shaft transmitting torque, or in way of the axial bearing where a roller bearing is used as a thrust bearing, is to be not less than 1,1 d _t. For thrust bearings located outside the gearcase see Pt 11, Ch 2, 2 Particulars to be submitted.

4.8.1 In general, arrangements are to be made so that the interior structure of the wheel may be examined. Alternative proposals will be specially considered.

4.9.1 For shafting external to the gearbox and other components ancillaries see Pt 11, Ch 2 Shafting Systems.

4.10.1 Where a clutch is fitted in the transmission, normal engagement shall not cause excessive stresses in the transmission or the driven machinery. Inadvertent operation of any clutch is not to produce dangerously high stresses in the transmission or driven machinery.

4.11.1 Gearcases and their supports are to be designed sufficiently stiff such that misalignment at the mesh due to movements of the external foundations and the thermal effects under all conditions of service do not disturb the overall tooth contact.

4.11.2 Inspection openings are to be provided at the peripheries of gearcases to enable the teeth of pinions and wheels to be readily examined. Where the construction of gearcases is such that sections of the structure cannot be readily be moved for inspection purposes, access openings of adequate size are also to be provided at the ends of the gearcases to permit examination of the structure of the wheels. Their attachment to the shafts is to be capable of being examined by removal of bearing caps or by equivalent means.

4.11.3 For gearcases fabricated by fusion welding the carbon content of the steels should generally not exceed 0,23 per cent. Steels with higher carbon content may be approved subject to satisfactory results from weld procedure tests.

4.11.4 Gearcases are to be stress relieved upon completion of all welding.

4.11.5 Gearcases manufactured from material other than steel will be considered upon full details being submitted.

4.12.1 The normal backlash between any pair of gears should not be less than:

4.12.2 The normal backlash is not to exceed three times the value calculated in Pt 11, Ch 1, 4.12 Backlash 4.12.1.

4.13.1 Reduction gears with sleeve bearings, for main and auxiliary purposes are to be provided with means for checking the internal alignment of the various elements in the gearcases.

4.13.2 In the case of separately mounted reduction gearing for main propulsion, means are to be provided by the gear manufacturer to enable the Surveyors to verify that no distortion of the gearcase has taken place, when chocked and secured to its seating on board the craft.