Page 218 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
196
where tooth form factor Y Fa and stress correction factor Y sa can be selected from
Table 8.4 by the virtual number of teeth z .
v
Contact ratio factor Y for bending stress calculation is calculated by [9]

0.75
Y = 0.25 + (8.58)

v
where is transverse contact ratio of virtual spur gear, calculated by [9, 15]
v

= (8.59)
v 2
cos
b
and the base circle helix angle can be obtained from [15]
b
√
cos = 1 −(sin cos ) 2 (8.60)
b n
Y is helix angle factor for bending stress calculation. It is introduced to consider the

influence of oblique lines of contact in a helical gear on the tooth root bending stress
and can be calculated by [15]

Y = 1 − ∘ (8.61)

120
∘
∘
where is the helix angle. If is greater than 30 ,select = 30 . is face contact ratio,

which is calculated by Eq. (8.40) and the value 1.0 is substituted for if > 1.0.

8.4.4.2 Bending Strength Analysis
For safe operation of a helical gear, the bending stress should not exceed the allowable
stress, that is
KF t
= Y Y Y Y ≤ [ ] (8.62)
F Fa Sa F
bm
n
If tooth strength is the main criterion determining load carrying capacity, let
F = 2T/d , = b/d and d = m z = m z /cos , the normal module of a helical gear
1
t
d
1
n 1
1
t 1
can be derived from Eq. (8.62) as,
√
2
2KT cos Y Y Y Y
Fa Sa
1
m ≥ 3 ⋅ (8.63)
n
z 2 [ ]
F
d 1
8.5 Strength Analysis for Bevel Gears
8.5.1 Geometry and Terminology
Bevel gears provide the most efficient methods of transmitting power between intersect-
ing shafts, usually at right angles. Notwithstanding the fact that bevel gears are more
complex than spur and helical gears in manufacturing and assembly, they find wide
applications for power transmission between intersecting shafts.
Bevel gears may have straight, spiral or other curvilinear teeth. The differences
between spiral and straight bevel gears is similar to those between helical and spur
gears. The spiral teeth have a gradual pitch line contact and a larger number of teeth
in contact. This make it possible to obtain smoother engagement and higher load