| M = D cos q + dw
(11) cos q1 For an odd number of teeth M = D cos q cos 90º + dw (12) cos q1 where the value of q1 is obtained from inv q1 = T + invq + dw - p (13) D D cos q N |
 |
The tooth thickness (T2) at a
given radius, R2, from the center can be found from a known value (T1)
and known
pressure angle (q1)
at that radius (R1), as follows:
T2 = T1 R2
- 2R2 -2R2 (inv q2 - inv q1)
(10)
R1
where:
inv q =tan q - q
= involute function.
To save computing time involute-function tables have been computed and are available in the references. An abridged liting is given in Table 1.5.
4.6 Measurement Over-Pins
Often tooth thickness is measured indirectly
by gaging over pins which are placed in diametrically opposed tooth spaces, or the nearest
to it for odd numbered gear teeth. This is pictured in Figure 1.15.
For a specified tooth thickness the
over-pins measurement, M, is calculated as follows:
For an even number of teeth:
| M = D cos q + dw
(11) cos q1 For an odd number of teeth M = D cos q cos 90º + dw (12) cos q1 where the value of q1 is obtained from inv q1 = T + invq + dw - p (13) D D cos q N |
|
Tabulated values of over-pins measurements for standard gears are given in Table 1.6. This
provides a rapid means for calculating values of M, even for gears with slight departures
trom standard tooth thicknesses.
When tooth thickness is to be
calculated from a known over-pins measurement, M, the equations can be manipulated to
yield:
T = D ( p + inv qc - inv q - dw )
(14)
N
D cos q
where:
cos qc = D cos q
(15)
2Rc
for an even number of teeth:
Rc = M - dw
(16)
2
and for an odd number of teeth:
Rc
= M - dw
(17)
2 cos 90º
N
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