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### Helical Gears Shafts Right Angles Approximate Design Equations and Calculator

Helical Gears Shafts at Right Angles Design Equations and Calculator Sum of helix angles of gear and pinion must equal 90 degrees.

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Number of teeth in pinion for any angle:

n = ( 2 Ca Pn cos α cos β ) / ( R cos β + cos α )

Number of teeth in gear formula:

N = n R

Pitch diameter of gear formula:

D = N / ( Pn cos α )

Pitch diameter of pinion formula:

d = n / ( Pn cos α )

Number of formed cutter (gear) Formula:

T = N / ( Pn cos3 α )

Number of formed cutter (pinion) Formula:

T = n / ( Pn cos3 α )

Lead of helix of gear formula:

L = π D cot α

Lead of helix of pinion formula:

l = π d cot β

Where:

C = approximate center distance (in, mm),
Pn  = normal diametral pitch (in, mm),
N = number of teeth in large gear,
n = number of teeth in small gear,
α = angle of gear helix (deg),
β = angle of pinion helix (deg),
R = ratio of gear to pinion,
L = lead of helix on large gear (in, mm),
l = lead of helix on pinion (in, mm).

References:

Machinerys Handbook, 29th Edition