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### Gears Shafts Right Angles Exact Helix Design Equations and Calculator

Helical Gears Shafts at Right Angles Exact Design Equations and Calculator - Gears will have same direction of helix. Sum of the helix angles will equal 90 degrees. Sum of helix angles of gear and pinion must equal 90 degrees.

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Design variables you should know:

• Position of gear having right- or left-hand helix depending on rotation and direction in which thrust is to be received,
• Pn = normal diametral pitch (pitch of cutter),
• R = ratio of number of teeth in large gear to number of teeth in small gear,
• αa = approximate helix angle of large gear,
• C = exact center distance.

Number of teeth in pinion for any angle:

n = ( 2 Ca Pn sin αa ) / ( 1 + R tan αa )

Number of teeth in large gear formula:

N = n R

Exact helix angle of large gear ( exact angle found by trial and varying R sec α + cosec α )

α is the exact  helix angle of large gear found by trial from the following equality
R sec α + cosec α = R / cos α + 1 / sin α = ( 2 C Pn ) / n

Exact helix angle of small gear

β = 90° - α

Pitch diameter of large gear

D = N / ( Pn cos α )

Pitch diameter of small gear

d = n / ( Pn cos β )

Outside diameter of large gear

O = D + 2 / Pn

Outside diameter of small gear

o = d + 2 / Pn

Lead of helix on karge gear formula:

L = π D cot α

Lead of helix on small gear 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