Machinery's Handbook, 31st Edition
2210 Gears and Gearing teeth on each gear, the increase in pitch diameter per tooth varies according to the pitch. For example, the pitch diameter of a gear having, say, 20 teeth of 4 diametral pitch will be 5 inches; 21 teeth, 5 1 ∕ 4 inches; and so on, the increase in diameter for each additional tooth being equal to 1 ∕ 4 inch for 4 diametral pitch. Similarly, for 2 diametral pitch the variations for successive numbers of teeth would equal 1 ∕ 2 inch, and for 10 diametral pitch the varia tions would equal 1 ∕ 10 inch, etc. Where a given center distance must be maintained and no standard diametral pitch can be used, gears should be designed with reference to the gear set center distance procedure discussed in Gears for Given Center Distance and Ratio starting on page 2218 . Table 1. Formulas for Dimensions of Standard Spur Gears To Find Formula To Find Formula Base Circle Diameter cos D D B φ = (1) Number of Teeth N P D # = (2a) Circular Pitch . p N D = 31416 (3a) . N p D = 31416 (3b) . p P = 31416 (3c) Outside Diameter (Full-depth Teeth) D P N 2 O = + (4a) 1 P G + ^ h h (5b)
. N p 31416 2
N m 2
O = + ^
(5a)
D
=
C
P
D D 2 P G = + N N 2 G P = + G P = + ^ h
(6a)
. D P N 16 O = +
(5c) Outside Diameter (American Standard Stub Teeth) (6b)
C
Center Distance
. N p 31416 16 . h
(6c)
O = + ^
D
C P
(7)
. N N p 62832
(6d) Outside Diameter D D a 2 O = +
C
(8a) (9b)
(9a) (9c) (10) (12) (13)
. P p = 31416
D P N =
Pitch Diameter
Np = 31416
P D N =
Diametral Pitch
D
.
1 P G
+ ^ h
N m 2
(9d) Root Diameter a
D D b 2 R = −
=
P
C
Whole Depth Working Depth
m N N G P G =
a b + a a G P +
(11)
Gear Ratio
a See also formulas in Table 2 and Table 4 on pages 2210 and 2214 . Table 2. Formulas for Tooth Parts, 20-and 25-degree Involute Full-depth Teeth ANSI Coarse Pitch Spur Gear Tooth Forms ANSI B6.1-1968 (R1974) To Find Diametral Pitch, P , Known Circular Pitch, p , Known Addendum a = 1.000 ÷ P a = 0.3183 × p Dedendum (Preferred) b = 1.250 ÷ P b = 0.3979 × p (Shaved or Ground Teeth) a b = 1.350 ÷ P b = 0.4297 × p Working Depth h k = 2.000 ÷ P h k = 0.6366 × p Whole Depth (Preferred) h t = 2.250 ÷ P h t = 0.7162 × p (Shaved or Ground Teeth) h t = 2.350 ÷ P h t = 0.7480 × p Clearance (Preferred) b c = 0.250 ÷ P c = 0.0796 × p (Shaved or Ground Teeth) c = 0.350 ÷ P c = 0.1114 × p
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