Machinery's Handbook, 31st Edition
2274
HELICAL GEARING HELICAL GEARING
Basic Rules and Formulas for Helical Gear Calculations.— The rules and formulas in the following table and elsewhere in this article are basic to helical gear calculations. The notation used in the formulas is: P n = normal diametral pitch of cutter; D = pitch diameter; N = number of teeth; α = helix angle; γ = center angle or angle between shafts; C = center distance; N ′ = number of teeth for which to select a formed cutter for milled teeth; L = lead of tooth helix; S = addendum; W = whole depth; T n = normal tooth thickness at pitch line; and O = outside diameter. Rules and Formulas for Helical Gear Calculations
α a
In the formulas, the symbols D , N , L and a are for either the gear or the pinion. Subscripts a and b refer to the pinion or gear, respectively, in a pair of gears a and b .
a
b
α a
α b
γ
α b
No.
To Find
Rule
Formula
1 Pitch Diameter
Divide the number of teeth by the product of the normal diameter pitch and the cosine of the helix angle.
D P N n =
cos
α
2 Center Distance Add together the two pitch diameters and divide by 2. C
D D 2 a +
=
b
3 Lead of Tooth Helix
Multiply the pitch diameter by 3.1416 by the cotangent of the helix angle.
L = π D cot α
4 Addendum Divide 1 by the normal diametral pitch.
S P 1 n =
5 Whole Depth of tooth 6 Normal Tooth Thickness at Pitch Line
Divide 2.157 by the normal diametral pitch.
. W P 2157 n = . T P 15708 n n =
Divide 1.5708 by the normal diametral pitch.
7 Outside Diameter Add twice the addendum to the pitch diameter. O = D + 2 S Determining Direction of Thrust.— The first step in helical gear design is to deter- mine the desired direction of the thrust. When the direction of the thrust has been de- termined and the relative positions of the driver and driven gears are known, then the direction of helix (right- or left-hand) may be found from the accompanying thrust diagrams, Directions of Rotation and Resulting Thrust for Parallel Shaft and 90 Degree Shaft Angle Helical Gears . The diagrams show the directions of rotation
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online