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 |
