Table 1c. Formulas for Calculating Dimensions of Helical Gears
Outside Diameter of Blank, O P A N A cos cos 2
Tooth Form and Pressure Angle
Normal Diametral Pitch, P N
Diametral Pitch, P O N A 2 or N + cos P A cos
Pitch Diameter, D
Cosine of Helix Angle, A
Addendum Dedendum Whole Depth
. 1157
N + +
. 2157
P
P 1 or N
cos O A N A # + cos
2 or
cos P A N N
P or N
P
P or N
American Standard 14 1 ∕ 2 - and 20-degree full depth
or N N # −
2 or
P N or
P
O P N
cos
cos P N A
2157
. cos
A
1157
. cos
A
A
cos
A
P
2
P
P
P
. 18
. 08
P 1 or N
+
. 16 or
cos
cos P A N N
+
. 16
cos
N
A
N
A
cos P A
. A 16 or n cos
cos O A #
P
P
P
. cos
P A N
N or N N # −
or N
or N
American Standard 20-degree stub
P N or
P 16 or
+
N
P
08
. cos
cos
18
. cos
A
A
A
+
cos
N
A
O
cos
A
. 16
P
P
P
O P
N
P 1 N D ^ h
2
. P 125 N D ^ h
. P 225 N D ^ h
cos P A N
cos P A N N N h
Fellows 20-degree stub
2
+
…
…
P O N N c h
^
−
h m
P
h
N N ^ h
^
^
P
^
N D
N D
P N = normal diametral pitch = normal diametral pitch of cutter or hob used to cut teeth P = diametral pitch O = outside diameter of blank D = pitch diameter A = helix angle N = number of teeth
(P N ) N = normal diametral pitch in numerator of stub-tooth designation, which determines thickness of tooth and number of teeth (P N ) D = normal diametral pitch in denominator of stub-tooth designation, which determines the addendum, dedendum, and whole depth
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