If, in Fig. 33.2, the distance from a to b exactly equals the base pitch, then, when
one pair of teeth are just beginning contact at a, the preceding pair will be leaving
contact at b. Thus, for this special condition, there is never more or less than one pair
of teeth in contact. If the distance ab is greater than the base pitch but less than twice
as much, then when a pair of teeth come into contact at a, another pair of teeth will
still be in contact somewhere along the line of action ab. Because of the nature of
this tooth action, usually one or two pairs of teeth in contact, a useful criterion of
tooth action, called the contact ratio mc) can be defined. The formula is
mc = Lab/ Pb (33.6)
where Lab = distance ab, the length of the line of action. Do not confuse the contact
ratio mc with the module m.
33.2 TOOTHDIMENSIONSANDSTANDARDS
The American Gear Manufacturer's Association (AGMA) publishes much valuable
reference data.f The details on nomenclature, definitions, and tooth proportions for
spur gears can be found in ANSI/AGMA 201.2 and 1012-F90. Table 33.2 contains the
most used tooth proportions. The hob tip radius rf varies with different cutters;
0.300/Prf or 0.300m is the usual value. Tables 33.3 and 33.4 list the modules and
pitches in general use. Cutting tools can be obtained for all these sizes.
See Chap. 35 for a special note on AGMA.
TABLE 33.2 Standard and Commonly Used Tooth Systems for Spur Gears
Tooth system Pressure angle 0, deg Addendum a Dedendum b
Full depth 20 l/Pd or\m 1.25/Pd or .25m
1..35/Pd or .35m毕业论文
http://www.youerw.com/221 i/ Pd or\m 1.25/Pd or1.25m/
1.35/ Pd or1.35m
25 1/Pd or\m 1.25/Pd or1 .25m
1.35/Pd or1 .35m
Stub 20 0.8/Pd or 0.8m 1/Pd or 1 m
TABLE 33.3 Diametral Pitches in General Use
Coarse pitch 2, 21 2J, 3, 4, 6, 8, 10, 12, 16
Fine pitch 20, 24, 32, 40, 48, 64, 96, 120, 150, 200
TABLE 33.4 Modules in General Use
Preferred 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50
Next choice 1.125, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5, 5.5, 7, 9, 11, 14, 18, 22, 28, 36, 45
33.3 FORCEANALYSIS
In Fig. 33.3 a gear, not shown, exerts force W against the pinion at pitch point R This
force is resolved into two components, a radial force Wr) acting to separate the gears,
and a tangential component Wt, which is called the transmitted load.
Equal and opposite to force W is the shaft reaction F, also shown in Fig. 33.3.
Force F and torque T are exerted by the shaft on the pinion. Note that torque T
opposes the force couple made up of Wt and Fx separated by the distance d/2. Thus
T =Wtd/2 (33.7)原文请+QQ3249,114优.文^论,文'网
Where T = torque, Ib • in (N • m)
Wt = transmitted load, Ib (N)
d = operating pitch diameter, in (m)
The pitch-line velocity v is given by
v=ndnP/12 ft/mim v= ndnP/60 m/s (33.8)FIGURE
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