Based on the fixed-end beam calculation. Includes the majority of effects.

Safety factor of contact fatigue

where:

	σ Hlim	contact fatigue limit (material value)
	F t	tangential force acting at teeth
	b w	operating facewidth

Safety factor of bending fatigue

where:

σ Flim

bending fatigue limit (material value)

Increase of Temperature Check

Safety against overheating: Q od ≥ P z

where:

	Q od = ϑ D A k	heat conducted away in oil
	ϑ D = t max - t 0 = 60o	available temperature drop
	A	gearbox surface, which conducts away the heat, A ≈ 9 . 10 -5 a 1.85 for well ribbed gearbox
	k	transfer of heat factor, k ≈ 6.6.10 -3 (1 + 0.4n 1 0.75 ) for the gearbox with fan and bottom worm

Deflection Check of Worm Shaft

Resultant deflection if the worm is symmetrically mounted and has the length l = 2.5 b 1 :

where:

		moment of inertia
	Allowable deflection:
	y D ≈ 0.004m	shaft with hardened worm
	y D ≈ 0.01m	shaft with heat-treated worm

Factor calculations

Z N ... service life (for contact)

1 ≤ ZN ≤ 1.8

Y N ... service life (for bending)

1 ≤ ZN ≤ 1.85

N Hlim , N Flim ... base number of load cycles (material value)

N K1,2 ... required number of load cycles (speed)

N K2 = 60 L h n 2

Z L ... lubricant

Z v ... circumferential speed

Z E ... material mechanical properties

where:

	μ	Poisson's ratio (material value)
	E	modulus of elasticity (material value)

Z H ... mating teeth shape

Z ε ... length of contact curves

Y ε ... profile mesh effect

for ε β < 1:
for ε β ≥ 1:

Y β ... helix direction

where:

Y β min = 1 - 0.25 ε β ≥ 0.75

Y F ... tooth shape (table value)

Z V	Y F
20	1.98
22	1.93
25	1.95
27	1.8
30	1.76
33	1.7
36	1.62
40	1.55
45	1.48
50	1.45
60	1.4
80	1.34
100	1.3
150	1.27
300	1.24

K H ... additional loads (for contact)

K H = K A K Hv K Hβ K Hα

K F ... additional loads (for bending)

K F = K A K Fv K Fβ K Fα

K A ... outside dynamic forces

where:

	K Hv = K Fv	table values
		portion of single tooth loading
		loading non uniform teeth along the width (for contact)
	Θ	worm deformation (table value)
		loading non uniform teeth along the width (for bending)
	h = 2 m