Machinery's Handbook, 31st Edition
Spur Gearing
2219
N
. N 15708 G
inv inv φ φ −
G
t
=
+
(8b)
c
m
P
1
2
G
The outside diameter of the pinion D PO and the gear D GO are
(9a)
D C D b P 2 2 1 PO GR c 1 1 # = − − − a k D C D b P 2 2 1 GO PR c 1 1 # = − − − a k
and (9b) Example: Design gears of 8 diametral pitch, 20-degree pressure angle, and 28 and 88 teeth to operate at 7.50-inch center distance. The gears are to be cut with a hob of 0.169-inch addendum. (1) . P 2 750 . 28 88 77333 1 # = + =
8 (
)
7.7333
1 φ = arccos
× 0.93969 = 24.719 °
(2)
28 3 6207 in.
P 1 =
=
.
D
(3a)
. 77333
88 11 3794 in.
.
G 1 =
=
D
and
(3b) (4a) (4b) (5) (6a)
. 77333
=
. 3 6207 0 90837 3 2889 in. . . # =
D
PB 1
. D 11 3794 0 90837 10 3367 in. GB 1 # = = . .
and
. . 77333 1 5708 0 20312 in. . =
1 =
t
. 8 28 2 0 1016 3 2968 in. . # = − = . 8 88 2 0 0428 11 0856 in. . # = − − = ^ h
D
PR 1
D
and
(6b)
GR 1
. 2 036397 02454 8 15708 . . # − . 2 036397 03505 8 15708 . . # −
e
o
(7a)
. 0169 = −
. 01016in.
b
=
P 1
e
o
(7b)
. 0169 = −
. 00428in.
b
=−
G 1
8 28 8 88
. 28 1 5708 0 028922 0 014904 0 2454 in. . + − = k . 88 1 5708 0 028922 0 014904 0 3505 in. . . . . . + − − k
t
a
P 2 =
(8a) (8b) (9a) (9b)
t
a
G 2 =
. 2 750 110856 2 0169 8 1 38264in. . . # = − − − = a k . 2 750 32968 2 0169 8 1 11 6152 in. . . . . # = − − − = a k
D
PO 1
D
GO 1
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