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 b₁:

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 n₂

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