Table 1b. Formulas for Calculating Dimensions of Milled Bevel Gears—90 degree Shafts a
Diametral Pitch b of Both Gear and Pinion, P
Tangent of Addendum Angle b
Tooth Form and Pressure Angle American Standard 14 1 ∕ 2 - and 20-degree full depth American Standard 20-degree stub
Tangent of Pitch Cone Angle of Gear, tan A
Tangent of Pitch Cone Angle of Pinion, tan a
Tangent of Dedendum Angle b
Cosine of Pitch-Cone Angle c of Gear, cos A
Outside Diameter of Gear, O , or Pinion, o
Pitch-Cone Radius b or Cone Distance, E
. 2314
sin
+
2
cos
2
sin N or a sin
A
+
P 2
cos
N
A
A
N
A
sin D
G
G
2
A
N
O 2 or
G
N N
N N
P O N 2 G # − ^ h
or
or
P 2 or
P G
G P
d
2
. 2314
sin
+
cos
a
a
+
cos
N
a
N
a
P
P
2
sin sin D
a
N
N
o
P
P
. 16
sin
+
. 16
cos
2
sin
A
+
. 16
cos
N
A
A
N
A
G
G
2
A
N
N
P
O
G
G
N N
N N
. P O N 16 G # − ^ h
or
or
or
. 16 or
. 16 or
P G
G P
2
sin
d
. 16
sin
+
cos
a
a
+
cos
N
a
N
a
P
P
2
sin
a
N
N
P
o
P
P
. 25
sin P A
sin N P P A 2 or G D N N # N P P D # sin P a 2
P N P N
sin D
2
cos
A
N P or G D N N # N P P D #
+
G
2
A
P
Fellows 20-degree stub
N
D
N N
N N
P P O P N 2 N D
N G # − ^ h 6 @
or
P G
…
G P
2 or
d
. 25
sin P a
cos
a
+
P
2
sin
a
P
N
D
a These formulas do not apply to Gleason System Gearing. b These values are the same for both gear and pinion. c The same formulas apply to the pinion, substituting N
P for N G and o for O . N G = number of teeth in gear; N P = number of teeth in pinion; O = outside diameter of gear; o = outside diameter of pinion; D = pitch diameter of gear = N G ÷ P ; d = pitch diameter of pinion = N P ÷ P ; P c = circular pitch; J = addendum; K = dedendum; W = whole depth. See footnote in Table 1a for meaning of P N and P D . The tooth thickness on the pitch circle is found by means of the formulas in the last column under spur gears.
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