Section 3 Design

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

Subscript:

3.2.1 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 0,25m _n.

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

3.3.1 For values of application factor, K _A see Table 5.3.1 Values of K _A .

3.3.2 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 5.3.2 Values of K _y may be considered:

3.3.3 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 5.3.3 Values of K ₁ .

   Table 5.3.3 Values of K ₁

   	K 1 ISO accuracy Grade
   	3	4	5	6	7	8
   Spur Gears	2,1	3,9	7,5	14,9	26,8	39,1
   Helical Gears	1,9	3,5	6,7	13,3	23,9	34,8

   For all accuracy grades the factor K₂ is to be in accordance with the following:

   • for spur gears K₂ = 0,0193
   • for helical gears K₂ = 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 _v = K_vα – ∊ β (K_vα – K_vβ )

   K _vα is the K_v value for spur gears, in accordance with (a)

   K _vβ is the K_v value for helical gears, in accordance with (b)

3.3.4 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

• y_β ≤ 6 μm

3.3.5 Transverse load distribution factors, K_Hα and K_Fα

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 K_Hα > when calculated in accordance with (a) or (b), then K_Hα =

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

   Limiting conditions for K_Fα:

   If K_Fα > when calculated in accordance with (a) or (b), then K _Fα

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

where

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

• y_α ≤ μm and

• y_α ≤ 3 μm

When pinion and wheel are manufactured from different materials:

3.3.6 Tooth mesh stiffness, C _γ:

For internal gears z _n2 = ∞

Other calculations methods for C _γ will be specially considered.

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

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 5.3.4 Values of C_ZR .

For values of Z_x, see Table 5.3.5 Values of Z_x

σ_{H lim}, see Table 5.3.6 Values of endurance limit for Hertzian contact stress, σ_{H lim}

S _{H min}, see Table 5.3.7 Factors of safety.

3.5.1 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 5.3.7 Factors of safety

σ_{F lim}, see Table 5.3.8 Values of endurance limit for bending stress, σ_{F lim}

Stress correction factor Y _ST = 2.

3.5.2 Tooth form factor, Y _F:

where h _F, α_{F en} and S_Fn are shown in Figure 5.3.1 Normal tooth section.

E, h_ao, α_n, S_pr and ρ_ao are shown in Figure 5.3.2 External tooth forms

3.5.3 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

3.5.4 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° but may be used as an approximation for other pressure angles and internal gears.

3.5.5 Helix angle factor Y_β

but Y _b ≥ 1 − 0,25 ε_b ≥ 0,75.

3.5.6 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 Y_B = 1,6∙ln

   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 Y_B = 1,15∙ln

   where

   S_R = rim thickness of internal gears, mm

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

3.5.7 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 ≤ 2,05 where:

Factor Y_DT is to be determined from Table 5.3.9 Values of deep tooth factor, Y _DT :

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

ρ’ = slip-layer thickness is to be taken from Table 5.3.10 Slip-layer thickness, ρ’

3.5.9 Relative surface finish factor, Y_{R rel T}

3.5.10 Size factor, Y _x

3.5.11 Design factor, Y_D

3.6.1 Factors of safety are shown in Table 5.3.7 Factors of safety.

3.7.1 This sub-Section is applicable to solid shafting enclosed within the gearcase of single input/single output gearing. Alternative configurations and hollow shaft designs, final gear wheel shafts and thrust shafts are to be in accordance with Pt 5, Ch 6, 3.3 Final gear wheel shafts and Pt 5, Ch 6, 3.4 Thrust shafts respectively.

3.7.2 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:

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

3.7.4 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.

3.7.5 For bevel gear shafts, where a bearing is located adjacent to the gear section, the diameter of the shaft is 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.