T-108
SECTION 11 CONTACT RATIO
To assure continuous smooth
tooth action, as one pair of teeth
ceases action a succeeding pair of
teeth must already have come into
engagement. It is desirable to have
as much overlap as is possible. A
measure of this overlap action is the
contact ratio. This is a ratio of the
length of the line-of-action to the
base pitch. Figure 11-1 shows the
geometry for a spur gear pair, which
i s t h e s i m p l e s t c a s e , a n d i s
representative of the concept for all
gear types. The length-of-action is
determined from the intersection of
the line-of-action and the outside
radii. The ratio of the length-of-
a c t i o n
t o
t h e
b a s e
p i t c h
i s
determined from:
–––––––––– ––––––––
Ö
(Ra
2
– Rb2) +
Ö
(ra
2
– rb2) – a sina
eg = –––––––––––––––––––––––––––––––––
(11-1)
pm cosa
It is good practice to maintain a contact ratio of 1.2 or greater. Under no circumstances
should the ratio drop below 1.1, calculated for all tolerances at their worst case values.
A contact ratio between 1 and 2 means that part of the time two pairs of teeth are in
contact and during the remaining time one pair is in contact. A ratio between 2 and 3 means 2
or 3 pairs of teeth are always in contact. Such a high ratio is generally not obtained with
external spur gears, but can be developed in the meshing of internal gears, helical gears, or
specially designed nonstandard external spur gears.
When considering all types of gears, contact ratio is composed of two components:
1.
Radial contact ratio (plane of rotation perpendicular to axes), ea
2.
Overlap contact ratio (axial), eb
The sum is the total contact ratio, eg
The overlap contact ratio component exists only in gear pairs that have helical or spiral tooth forms.
11.1 Radial Contact Ratio
Of Spur And Helical Gears, ea
The equations for radial (or plane of rotation) contact ratio for spur and helical gears are
given in Table 11-1, with reference to Figure 11-2.
When the contact ratio is inadequate, there are three means to increase it. These are
somewhat obvious from examination of Equation (11-1).
Decrease the pressure angle. This makes a longer line-of-action as it extends through
the region between the two outside radii.
Increase the number of teeth. As the number of teeth increases and the pitch diameter
grows, again there is a longer line-of-action in the region between the outside radii.
Increase working tooth depth. This can be done by adding addendum to the tooth and
thus increase the outside radius. However, this requires a larger dedendum, and
requires a special tooth design.
Fig. 11-1 Geometry of Contact Ratio
1.
2.
3.
a
Ra
Rb
a
B
A
T'
Z
B
W
T
rb
a
ra
WZ = Length-of-Action
BZ = AB = Base Pitch
