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Torque in Gear Drives Formulas

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Torque in Gear Drives Formulas

The lever arm of a gear is half of its reference diameter d. Different torques result if twoengaging gears do not have the same number of teeth.

Torque formulas;

M₁ = ( F_t1 · d₁ ) / 2

M₂ = ( F_t2 · d₂ ) / 2

M₂ = i · M₁

M₂ / M₁ = z₂ / z₁

M₂ / M₁ = n₂ / n₁

Driving Gear declarations

F_t1 = tangential force,
M₁ = torque,
d₁ = reference diameter,
z₁ = number of teeth,
n₁ = ratational speed.

Driven Gear declarations

F_t1 = tangential force,
M₁ = torque,
d₁ = reference diameter,
z₁ = number of teeth,
n₁ = rotational speed.

Driving and Driven Gear declaration

i = gear ratio

References:

Mechanical and Metal Trades Handbook, 2nd Edition
2010
Ulrich Fischer, Roland Gomeringer, Max Heinzler, Roland Kilgus, Friedrich Naher, Stefan Oesterle, Heinz Paetzold, Andreas Stephan

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