Based on the fixed-end beam calculation. Contains the majority of effects. Accessible only for metric units.

Safety factors

Contact fatigue

where:

	σ Hlim	base number of load cycles for contact (material property)
	F t	tangential force acting at teeth
	b w	operating face width

Contact during one-time loading

where:

	σ HPmax	contact fatigue limit (material property)
	K AS	one-time overloading factor

Bending fatigue

where:

	σ Flim	bending fatigue limit (material property)
	b wF1,2 = b	tooth width for bending

Bending during one-time loading

where:

σ FPmax

allowable bending stress in dedendum (material property)

Factor calculations

Z N ... life factor (for contact)

1 ≤ Z N ≤ 1.3 nitridated steels

1 ≤ Z N ≤ 1.6 other steels

where:

	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 ≤ Z Y ≤ 1.6 nitridated steels

1 ≤ Z Y ≤ 2.5 other steels

where:

	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
		pro σ Hlim < 850 Mpa C ZL = 0.83
		pro 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 value)
	E	modulus of elasticity (material value)

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:
for ε β ≥ 1:
	Z B1,2 = Z B0 - εβ(Z B0 - 1)
	where: Z B0 = Z B1,2 for ε β = 0

Z ε ... contact ratio factor (for contact)

for ε β = 0:
for ε β < 1:
for ε β ≥ 1:

Y ε ... contact ratio factor (for bending)

CSN: for ε β < 1:
CSN: for ε β ≥ 1:
DIN and ISO:

Z β ... helix angle (for contact)

Y β ... helix angle factor (for bending)

CSN:
	Y βmin = 1 - 0.25 ε β ≥ 0.75
DIN and ISO
	for ε β > 1 the ε β = 1 is used
	for β > 30 deg. the β = 30 deg.is used

Z x ... size factor (for contact)

Y x ... size factor (for bending)

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 concentration during mesh by tooth end (regression function)

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 DIN and ISO:	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

	f ky = | f sh1 + f sh2 | + f kZ - y β
	f b , f x , f y ... teeth tolerance
	y β ... table value
	q' = 0.04723 + 0.15551/z v1 + 0.25791/z v2 - 0.00635 x 1 - 0.11654 x 1 /z v1 - 0.00193 x 2 - 0.24188 x 2 /z v2 + 0.00529 x 1 2 + 0.00182 x 2 2
	C M = 0.8
	C R = 1 for solid gears
	C B = [1 + 0.5 (1.2 - h f /m)] [1 - 0.02 (20 deg.- α)]
	E steel = 206 000
	c γ = c' (0.75 ε α + 0.25)
	A, B ... table values depend on the arrangement of teeth gears, shafts, and bearings

K Fβ ... face load factor (for bending)

CSN:

K Fβ = (K Hβ ) NF

where:

	h = 2 m/ε α	spur gears
	h = 2 m	helical gears

for DIN and ISO:

K Fβ = K Hβ

K Fa ... transverse load factor (for bending)

for ε γ < 2:
for ε γ > 2:
	at K A F t / b w < 100 considering K A F t / b w = 100
limit values:
	for CSN: 1 ≤ K Fα ≤ε γ
	for DIN and ISO:

K Hα ... transverse load factor (for contact)

for CSN:	K Hα = 1 for straight teeth
	K Hα = K Fα for helical teeth
for DIN and ISO:	K Hα = K Fα
limit values: