Based on the fixed-end beam calculation. Contains the majority of effects.
Safety factors
Contact fatigue
where:
σ Hlim | contact fatigue limit (material property) | |
F t | tangential force acting at teeth | |
b w | operating face width | |
d 1 | pitch diameter of pinion |
Contact during one-time loading
where:
σ HPmax | permissible contact stress | |
K AS | one-time overloading factor |
Bending fatigue
where:
σ Flim | bending fatigue limit (material property) | |
b wF1,2 = min (b 1,2 , b w + 2m) | tooth width for bending |
Bending during one-time loading
where:
σ FPmax | permissible bending stress |
Factor calculations
Z N ... life factor (for contact)
1 ≤ Z N ≤ 1.3 nitridated steels
1 ≤ Z N ≤ 1.6 other steels
N Hlim | base number of load cycles for contact (material property) | |
N K1,2 = 60 L h n 1,2 | required number of load cycles (speed) |
Y N ... life factor (for bending)
1 ≤ Y N ≤ 1.6 nitridated steels
1 ≤ Y N ≤ 2.5 other steels
N Flim | base number of load cycles for bending (material property) | |
N K1,2 = 60 L h n 1,2 | required number of load cycles (speed) |
Z L ... lubricant factor
DIN and ISO: | ||
Z L = C ZL + 4 (1 - C ZL ) 0.158 | ||
C ZL = σ Hlim / 4375 + 0.6357 | ||
for σ Hlim < 850 Mpa C ZL = 0.83 | ||
for σ Hlim > 1200 Mpa C ZL = 0.91 |
Z R ... roughness factor
Z V ... speed factor
CSN: | ||
Z v = 0.95 + 0.08 log v | ||
ISO and DIN: | ||
C ZV = C ZL + 0.02 |
Z E ... elasticity factor
where:
μ | Poisson's ratio (material property) | |
E | modulus of elasticity (material property) |
Z H ... zone factor
Z B ... single pair tooth contact factor
for ε β ≥ 1 or internal gearing: | |
Z B1,2 = 1 | |
for ε β = 0: | |
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for ε β < 1: | |
Z B1,2 = Z B0 - ε b (Z B0 - 1) where: | |
Z B0 = Z B1,2 calculated for ε β = 0 |
Z ε ... contact ratio factor
for ε β = 0: | |
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for ε β < 1: | |
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for ε β ≥ 1: | |
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Y ε ... contact ration factor (for bending)
CSN:
for ε β < 1: | | |
for ε β ≥ 1: | |
ISO and DIN:
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Z β ... helix angle factor (for contact)
CSN:
Z β = 1 |
ISO and DIN:
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Y β ... helix angle factor (for bending)
CSN:
Y βmin = 1 - 0.25 ε β ≥ 0.75 |
ISO and DIN:
for ε β > 1 the ε β = 1 is used | |
for β > 30° the β = 30° is used |
Z x ... size factor (for contact)
Y x ... size factor (for bending)
Z W ... work hardening factor
Y Fa ... form factor
where:
h Fa | bending arm of a force acting on the tooth end | |
s Fn | thickness of dedendum dangerous section of alternate gear | |
α Fan | bending angle at the end of straight tooth of alternate gear |
Y Sa ... stress correction factor
Y Sa = (1.2 + 0.13 L a ) q s exp
Y Sag ... teeth with grinding notches factor
Y δ ... notch sensitivity factor (depends on the material and curvature radius of dedendum transition)
Y R ... tooth root surface factor
K H ... additional loads factor (for contact)
K H = K A K Hv K Hb K Ha
K F ... additional loads factor (for bending)
K F = K A K Fv K Fb K Fa
K A ... application factor (external dynamic forces)
K Hv ... dynamic factor (internal dynamic forces) for contact
K Fv ... dynamic factor (internal dynamic forces) for bending
for CSN:
at K A F t / b w < 150 considering K A F t / b w = 150 |
for ISO and DIN:
at K A F t / b w < 100 considering K A F t / b w = 100 | |
where: K P , K Q ... table values |
K Hβ ... face load factor (for contact)
for CSN:
where:
c = 0.4 | gears with hardened tooth sides | |
c = 0.3 | non-hardened gears | |
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f ky = | f sh1 + f sh2 | + f kZ - y β | ||
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f b , f x , f y ... teeth tolerance y β ... table value | ||
for ISO and DIN:
for | ![]() | |
otherwise ( < 1): | | |
F βy = F βx χ β | ||
for gears with hardened tooth sides χ β = 0.85 | ||
for others | | |
F βx = 1.33 f sh + f ma |
K Fβ ... face load factor (for bending)
K Fβ = (K Hβ ) NF
where:
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h = 2 m/ε α | spur gears | |
h = 2 m | helical gears |
K Fa ... transverse load factor (for bending)
for ε γ < 2: | |
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for ε γ > 2: | |
at K A F t / b w < 100 considering K A F t / b w = 100 | |
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limit values: | |
for CSN: 1 ≤ K Fα ≤ε γ | |
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K Hα ... transverse load factor (for contact)
for CSN: | |
K Hα = 1 for straight teeth | |
K Hα = K Fα for helical teeth | |
DIN and ISO: | |
K Hα = K Fα | |
for limit values: | |
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