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

**Machine Design and Engineering**

**Mechanical Gear Design and Engineering**

**Helical Gears Shafts at Right Angles Design Equations and Calculator**

Sum of helix angles of gear and pinion must equal 90 degrees.

Related:

Helical Gears Shafts Parallel Center Distance Exact Design Equations and Calculator

Helical Gears Shafts Parallel Center Distance Approximate Design Equations and Calculator

Preview ** Helical Gears Shafts at Right Angles Design Calculator**

Number of teeth in pinion for any angle:

n = ( 2 C_{a} P_{n} 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 / ( P_{n} cos α )

Pitch diameter of pinion formula:

d = n / ( P_{n} cos α )

Number of formed cutter (gear) Formula:

T = N / ( P_{n} cos^{3} α )

Number of formed cutter (pinion) Formula:

T = n / ( P_{n} cos^{3} 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),

P_{n} = 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