| 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 is the simplest case, and is
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 action to the base pitch is determined
from:
(11-1)
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 ell 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
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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). 1. Decrease the pressure angle. This makes a longer line-of action as it extends through the region between the two outside radii. |
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2. 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. An example of helical gear:
Note that in Table 11-1 only the radial or circular (plane of rotation) contact ratio is considered. This is true of both the spur and helical gear equations. However, for helical gears this is only one component of two. For the helical gears total contact ratio, eg, the overlap (axial) contact ratio, eb must be added. See Paragraph 11.4. 11.2 Contact Ratio Of Bevel Gears, ea The contact ratio of a
bevel gear pair can be derived from consideration of the eqivalent spur
gears, when viewed from the back cone. See Figure 8-8.
11.3 Contact Ratio For Nonparallel And Nonintersecting Axes Pairs, e This group pertains to screw gearing and worm gearing. The equations are approximations by considering the worm and worm gear mesh in the plane perpendicular to worm gear axis and likening it to spur gear and rack mesh. Table 11-3 presents these equations. Example of worm mesh:
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