Page 213 - Analysis and Design of Machine Elements

Centre distance is Gear Drives 191
1 m n
a = (d + d )= (z + z ) (8.35)
1
2
2
1
2 2cos
The relationship between transverse and normal pressure angle is [13]
tan n
tan = (8.36)
t
cos
From Figure 8.7, the helix angle is
d
tan =
l
Similar, the base circle helix angle is
b
d b
tan =
b
l
Therefore, the relationship between helix angle and base circle helix angle is [13]
b
tan = tan cos t (8.37)
b
For a pair of helical gears mounted on parallel shafts to mesh properly, they must have
the same module and pressure angle, as well as the same yet opposite helical angle.
8.4.1.2 Contact Ratio
When a pair of spur gears engage, the line of contact is initially near the tip of driven
gear tooth across the face width. It then moves smoothly along the involute profile to

the root of driven gear tooth where the mating teeth separate as the gears continue to
rotate. The contact length actually changes from one face width to two face widths and
back. Comparatively, when a pair of helical gears engage, the contact line is incline due
to helix angle and the contact length changes smoothly from minimum to maximum
as the gears rotate, leading to a gradual and smooth engagement. The contact ratio of a
helical gear drive is normally much higher than that of a spur gear drive.
The contact ratio of a helical gear drive is a measure of overall load sharing among the
teeth in contact. It is the sum of two contributions, transverse contact ratio and face
a
contact ratio, or overlap ratio ,expressed as

= + (8.38)
a
Since tooth profiles are involute in the transverse plane, the transverse contact ratio
is calculated in the transverse plane by means similar to that of a spur gear drive. Trans-
verse contact ratio reflects the load sharing among multiple teeth simultaneously in
contact, which can be obtained by Eq. (8.10) or estimated by [12]
[ ( )]
1 1
= 1.88 − 3.2 ± cos (8.39)

z 1 z 2
The positive sign is used for external gears and the negative for internal gears.
The face contact ratio is the contact ratio in the axial or face direction. It corresponds
to distribution of tooth loading along the contact length. The face contact ratio closely
relates to face width and helix angle, from Figure 8.7, we have
b b sin
= = = 0.318 z tan (8.40)
d 1
p m
a n